ecosystemSize
Emanuele Giacomuzzo
2024-10-02 08:44
## [1] "!! low !! The experiment investigate the effects of two disturbance levels: low and high. To make it easier to interpet, we showcase only one of the two disturbance levels. In this document we showcase only the low disturbance)"Design
Ecosystem size is a key factor driving biodiversity and ecosystem function. Larger ecosystems contain more species and can be hubs of dispersal and resource flows in networks of multiple ecosystems. However, whether and how ecosystem size and resource flows interact to affect biodiversity and ecosystem function has been largely overlooked. Here, we investigated how ecosystem size asymmetry affects biodiversity and function of two-ecosystem meta-ecosystems connected through flows of non-living resources. We conducted microcosm experiments, mimicking resource flows between ecosystems of different sizes, yet otherwise being identical. We found that meta-ecosystems with asymmetric ecosystem sizes had higher β-diversity but lower α-diversity and ecosystem function (total biomass) than their unconnected counterparts, while such an effect was not found for meta-ecosystems of identical ecosystem sizes. Our work demonstrates of how cross-ecosystem dynamics modulated by differences in ecosystem sizes affect biodiversity and function, with a direct implication for conservation and management of connected ecosystems.
Parameters
Parameters for R markdown and the general running of the code.
start_time = Sys.time()
knitr::opts_chunk$set(message = FALSE,
cache = FALSE,
autodep = FALSE)
recompute_lengthy_analyses = FALSE
plot_model_residuals_metaecos = FALSEParameters related to resource flows.
disturbance_levels = c("low", "high")
n_disturbance_levels = length(disturbance_levels)
resource_flow_days = c(5, 9, 13, 17, 21, 25)
first_resource_flow = resource_flow_days[1]Parameters related to sampling.
total_frames = 125
volume_recorded_μl = 34.4
time_points = 0:7
time_points_without_t0 = 1:7
time_point_names = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")
sampling_days = c(0, 4, 8, 12, 16, 20, 24, 28)
first_time_point = 0
last_time_point = length(sampling_days) - 1
n_time_points = last_time_point + 1
nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2) #Videos taken for each time point for each culture. At t0 we took 12 videos of the large bottle from which we started the cultures. Write why 2 at the end.
videos_taken = data.frame(time_point = 0 : 7,
nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2))
n_videos_taken_t0 = nr_videos[1]
time_point_day = data.frame(time_point = first_time_point:last_time_point,
day = sampling_days,
video_replicates = nr_videos)
videos_to_take_off = data.frame(culture_ID = NA,
time_point = NA,
file = NA) %>%
add_row(culture_ID = 137-110,
time_point = 7,
file = 137) %>%
slice(-1)
n_cultures = 110
total_number_of_video_rows = sum(nr_videos * n_cultures)Parameters related to protists.
protist_species = c("Ble", "Cep", "Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi", "Spi_te", "Tet")
protist_species_indiv_per_volume = paste0(protist_species, "_indiv_per_volume")
protist_species_indiv_per_ml = paste0(protist_species, "_indiv_per_ml")
protist_species_dominance = paste0(protist_species_indiv_per_ml, "_dominance")
protist_species_total = paste0(protist_species, "_tot_indiv")
n_protist_species = length(protist_species)
first_protist = protist_species[1]
last_protist = protist_species[n_protist_species]
species_IDD_with_13_threshold = c("Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi_te", "Tet")
species_IDD_with_13_threshold_indiv_per_volume = paste0(species_IDD_with_13_threshold, "_indiv_per_volume")
species_IDD_with_40_threshold = c("Ble", "Cep", "Spi")
species_IDD_with_40_threshold_indiv_per_volume = paste0(species_IDD_with_40_threshold, "_indiv_per_volume")Parameters related to ecosystems.
ecosystems_to_take_off = 60 #Culture ID = 60 as it was spilled (small unconnected, high disturbance, system nr = 40)
ecosystems_info = read.csv(here("2_data", "ecosystems_info.csv"), header = TRUE)
columns_ecosystems = c("time_point",
"day",
"culture_ID",
"system_nr",
"disturbance",
"ecosystem_type",
"connection",
"ecosystem_size",
"ecosystem_size_ml",
"metaecosystem",
"metaecosystem_type")
columns_treatments = columns_ecosystems[!columns_ecosystems %in% c("system_nr", "culture_ID")]
variables_ecosystems = c("bioarea_mm2_per_ml",
"bioarea_tot_mm2",
"indiv_per_ml",
"indiv_tot",
"species_richness",
"shannon",
"simpson",
"inv_simpson",
"evenness_pielou",
"median_body_area_µm2",
paste0(protist_species, "_indiv_per_ml"),
paste0(protist_species, "_tot_indiv"),
paste0(protist_species_indiv_per_ml, "_dominance"))
baseline_columns = paste0("baseline_", variables_ecosystems)
ecosystem_types_ordered = c("Small connected to large",
"Small connected to small",
"Small unconnected",
"Medium connected to medium",
"Medium unconnected",
"Large connected to small",
"Large connected to large",
"Large unconnected")
treatments_and_controls = data.frame(treatment = c("Small connected to small",
"Small connected to large",
"Medium connected to medium",
"Large connected to large",
"Large connected to small"),
control = c("Small unconnected",
"Small unconnected",
"Medium unconnected",
"Large unconnected",
"Large unconnected"))
n_treatments = length(unique(treatments_and_controls$treatment))
n_controls = length(unique(treatments_and_controls$control))
n_replicates = 5
n_ecosystem_types = 8Parameters related to size classes.
n_size_classes = 12
columns_classes = c(columns_ecosystems,
"size_class_n",
"mean_class_area_µm2")Parameters related to meta-ecosystems.
metaecosystems_to_take_off = ecosystems_info %>%
filter(culture_ID %in% ecosystems_to_take_off) %>%
pull(system_nr) %>%
unique
system_nr_metaecosystems = ecosystems_info %>%
filter(metaecosystem == "yes") %>%
pull(system_nr) %>%
unique
n_metaecosystems = length(system_nr_metaecosystems)
variables_metaecos = c(
"total_metaecosystem_bioarea_mm2",
"jaccard_index",
"bray_curtis",
"beta_spatial_turnover",
"beta_nestedness",
"beta_total",
"metaecosystem_richness")
metaecosystem_types_ordered = c(
"Small-Small meta-ecosystem",
"Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Large-Large meta-ecosystem",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Name of the axes per response variable.
axis_names = data.frame(variable = NA,
axis_name= NA) %>%
add_row(variable = "day", axis_name = "Time (day)") %>%
add_row(variable = "ecosystem_size_ml", axis_name = "Patch size (ml)") %>%
add_row(variable = "log_size_class", axis_name = "Log size (μm2)") %>%
add_row(variable = "class_indiv_per_µl", axis_name = "Density (ind/ml)") %>%
add_row(variable = "bioarea_mm2_per_ml", axis_name = "Biomass (mm2/ml)") %>%
add_row(variable = "bioarea_mm2_per_ml_d", axis_name = "Bioamass ES") %>%
add_row(variable = "bioarea_tot", axis_name = "Total Biomass (mm2)") %>%
add_row(variable = "total_metaecosystem_bioarea_mm2", axis_name = "Total Biomass (mm2)") %>%
add_row(variable = "species_richness", axis_name = "Species Richness") %>%
add_row(variable = "species_richness_d", axis_name = "Species Richness ES") %>%
add_row(variable = "mean_richness", axis_name = "Mean α-Diversity (Shannon)") %>%
add_row(variable = "mean_shannon", axis_name = "Mean α-Diversity (Shannon)") %>%
add_row(variable = "shannon", axis_name = "Biodiversity (Shannon)") %>%
add_row(variable = "shannon_d", axis_name = "Biodiversity ES (Shannon ES)") %>%
add_row(variable = "bray_curtis", axis_name = "β-Diversity (Bray-Curtis)") %>%
add_row(variable = "beta_spatial_turnover", axis_name = "Turn over (Simpson pair-wise dissimilarity)") %>%
add_row(variable = "beta_nestedness", axis_name = "Nestedness (nestedness-fraction of Sorensen)") %>%
add_row(variable = "beta_total", axis_name = "Tot β-Diversity (Sorensen)") %>%
add_row(variable = "metaecosystem_richness", axis_name = "γ-Diversity (Species Richness)") %>%
add_row(variable = "indiv_per_ml", axis_name = "Abundance (ind/ml)") %>%
add_row(variable = "indiv_per_ml_d", axis_name = "Abundance ES") %>%
add_row(variable = "median_body_area_µm2", axis_name = "Median Body Size (µm²)") %>%
add_row(variable = "median_body_area_µm2_d", axis_name = "Median Body Size ES") %>%
add_row(variable = "Ble_indiv_per_ml", axis_name = "Ble Density (ind/ml)") %>%
add_row(variable = "Cep_indiv_per_ml", axis_name = "Cep Density (ind/ml)") %>%
add_row(variable = "Col_indiv_per_ml", axis_name = "Col Density (ind/ml)") %>%
add_row(variable = "Eug_indiv_per_ml", axis_name = "Eug Density (ind/ml)") %>%
add_row(variable = "Eup_indiv_per_ml", axis_name = "Eup Density (ind/ml)") %>%
add_row(variable = "Lox_indiv_per_ml", axis_name = "Lox Density (ind/ml)") %>%
add_row(variable = "Pau_indiv_per_ml", axis_name = "Pau Density (ind/ml)") %>%
add_row(variable = "Pca_indiv_per_ml", axis_name = "Pca Density (ind/ml)") %>%
add_row(variable = "Spi_indiv_per_ml", axis_name = "Spi Density (ind/ml)") %>%
add_row(variable = "Spi_te_indiv_per_ml", axis_name = "Spi te Density (ind/ml)") %>%
add_row(variable = "Tet_indiv_per_ml", axis_name = "Tet Density (ind/ml)") %>%
add_row(variable = "auto_hetero_ratio", axis_name = "Photosynthetisers-Heterotrops Ratio") %>%
add_row(variable = "Ble_indiv_per_ml_d", axis_name = "Ble Density ES") %>%
add_row(variable = "Cep_indiv_per_ml_d", axis_name = "Cep Density ES") %>%
add_row(variable = "Col_indiv_per_ml_d", axis_name = "Col Density ES") %>%
add_row(variable = "Eug_indiv_per_ml_d", axis_name = "Eug Density ES") %>%
add_row(variable = "Eup_indiv_per_ml_d", axis_name = "Eup Density ES") %>%
add_row(variable = "Lox_indiv_per_ml_d", axis_name = "Lox Density ES") %>%
add_row(variable = "Pau_indiv_per_ml_d", axis_name = "Pau Density ES") %>%
add_row(variable = "Pca_indiv_per_ml_d", axis_name = "Pca Density ES") %>%
add_row(variable = "Spi_indiv_per_ml_d", axis_name = "Spi Density ES") %>%
add_row(variable = "Spi_te_indiv_per_ml_d", axis_name = "Spi te Density ES") %>%
add_row(variable = "Tet_indiv_per_ml_d", axis_name = "Tet Density ES") %>%
add_row(variable = "Ble_indiv_per_ml_dominance", axis_name = "Ble Dominance (%)") %>%
add_row(variable = "Cep_indiv_per_ml_dominance", axis_name = "Cep Dominance (%)") %>%
add_row(variable = "Col_indiv_per_ml_dominance", axis_name = "Col Dominance (%)") %>%
add_row(variable = "Eug_indiv_per_ml_dominance", axis_name = "Eug Dominance (%)") %>%
add_row(variable = "Eup_indiv_per_ml_dominance", axis_name = "Eup Dominance (%)") %>%
add_row(variable = "Lox_indiv_per_ml_dominance", axis_name = "Lox Dominance (%)") %>%
add_row(variable = "Pau_indiv_per_ml_dominance", axis_name = "Pau Dominance (%)") %>%
add_row(variable = "Pca_indiv_per_ml_dominance", axis_name = "Pca Dominance (%)") %>%
add_row(variable = "Spi_indiv_per_ml_dominance", axis_name = "Spi Dominance (%)") %>%
add_row(variable = "Spi_te_indiv_per_ml_dominance", axis_name = "Spi te Dominance (%)") %>%
add_row(variable = "Tet_indiv_per_ml_dominance", axis_name = "Tet Dominance (%)") %>%
add_row(variable = "Ble_indiv_per_ml_dominance_d", axis_name = "Ble Dominance ES") %>%
add_row(variable = "Cep_indiv_per_ml_dominance_d", axis_name = "Cep Dominance ES") %>%
add_row(variable = "Col_indiv_per_ml_dominance_d", axis_name = "Col Dominance ES") %>%
add_row(variable = "Eug_indiv_per_ml_dominance_d", axis_name = "Eug Dominance ES") %>%
add_row(variable = "Eup_indiv_per_ml_dominance_d", axis_name = "Eup Dominance ES") %>%
add_row(variable = "Lox_indiv_per_ml_dominance_d", axis_name = "Lox Dominance ES") %>%
add_row(variable = "Pau_indiv_per_ml_dominance_d", axis_name = "Pau Dominance ES") %>%
add_row(variable = "Pca_indiv_per_ml_dominance_d", axis_name = "Pca Dominance ES") %>%
add_row(variable = "Sp_indiv_per_mli_dominance_d", axis_name = "Spi Dominance ES") %>%
add_row(variable = "Spi_te_indiv_per_ml_dominance_d", axis_name = "Spi te Dominance ES") %>%
add_row(variable = "Tet_indiv_per_ml_dominance_d", axis_name = "Tet Dominance ES") %>%
add_row(variable = "dominance", axis_name = "Dominance (%)") %>%
add_row(variable = "log_abundance", axis_name = "Log Abundance + 1 (ind/mm²)") %>%
add_row(variable = "abundance_hedges_d", axis_name = "Density ES") %>%
add_row(variable = "beta_diversity_from_unconnected", axis_name = "Divergence from unconnected") %>%
add_row(variable = "beta_diversity_from_previous_time", axis_name = "Temporal Divergence") %>%
add_row(variable = "beta_diversity_from_previous_time_d", axis_name = "Temporal Divergence ES") %>%
add_row(variable = "evenness_pielou", axis_name = "Evenness") %>%
add_row(variable = "evenness_pielou_d", axis_name = "Evenness ES") %>%
slice(-1)Colour and line type per ecosystem/meta-ecosystem type.
treatment_colours = c("Small" = "#feb24c",
"Medium" = "#1b7837",
"Large" = "#3182bd",
"Small-Small" = "#fc9272",
"Large-Large" = "#67000d",
"Small-Large" = "#762a83",
"Medium-Medium" = "#1b7837",
"symmetric" = "#1b7837",
"asymmetric" = "#762a83")
treatment_linetype = c("connected to small" = "solid",
"connected to medium" = "dashed",
"connected to large" = "longdash",
"connected" = "solid",
"unconnected" = "dotted")Parameters for plotting.
figures_height_rmd_output = 7
legend_position = "top"
legend_width_cm = 2
size_legend = 12
size_x_axis = 13
size_y_axis = size_x_axis
boxplot_width = 2
dodging = 0.5
width_errorbar = 0.2
dodging_error_bar = 0.5
treatment_lines_linewidth = 1
treatment_points_size = 2.5
resource_flow_line_type = "solid"
resource_flow_line_colour = "#d9d9d9"
resource_flow_line_width = 0.3
zero_line_colour = "grey"
zero_line_line_type = "dotted"
zero_line_line_width = 0.5
zero_line_ES_line_type = "dotted"
zero_line_ES_colour = "grey"
zero_line_ES_line_width = 1
ggarrange_margin_top = 0
ggarrange_margin_bottom = 0
ggarrange_margin_left = 0
ggarrange_margin_right = 0
paper_width = 17.3
paper_height = 20
paper_units = "cm"
paper_res = 600
paper_y_axis_size = 9
paper_labels_size = 9
presentation_figure_size = 15
presentation_figure_width = 30
presentation_figure_height = 22
presentation_legend_size = 20
presentation_x_axis_size = 22
presentation_y_axis_size = presentation_x_axis_size
presentation_axes_size = 12
presentation_treatment_points_size = 5
presentation_treatment_linewidth = 2
presentation_figure_units = "cm"
presentation_figure_res = 600
grey_background_xmin = -Inf
grey_background_xmax = 7.5
grey_background_ymin = -Inf
grey_background_ymax = Inf
grey_background_fill = "#f0f0f0"
grey_background_alpha = 0.03
grey_background_color = "transparent"Parameters for modelling.
time_point_of_baselines = 1
time_points_with_water_addtion = 3:7
time_points_model = time_points_with_water_addtion
optimizer_input = 'Nelder_Mead'
method_input = ''Data
Ecosystems information (ecosystems_info)
We start by importing the information about the 110 ecosystems of the experiment.
ecosystems_info = read.csv(here("2_data", "ecosystems_info.csv"), header = TRUE)Individuals (ds_individuals)
In this dataset (ds_individuals) each row represents an
individual at a time point.
# Import the individual data of t0. We considered cultures to be all the same at the beginning (t0). Because of this reason, we filmed only the bottles from which cultures were assembled. Because we want to plot also t0 for the different treatments, we want to assign the video of bottles to all cultures at t0.
ds_individuals_t0_not_elongated = read.csv(here("2_data",
"individuals_13_threshold",
"t0.csv")) %>%
mutate(time_point = as.numeric(str_extract(time_point, "\\d+")),
day = 0,
file = as.numeric(str_extract(file, "\\d+")),
video_replicate = file) %>%
select(time_point,
day,
video_replicate,
file,
id,
N_frames,
mean_area)
ds_individuals_t0_elongated = ds_individuals_t0_not_elongated %>%
map_dfr(.x = 1 : nrow(ecosystems_info),
.f = ~ ds_individuals_t0_not_elongated) %>%
arrange(id) %>% #Id refers to an individual
mutate(culture_ID = rep(1 : nrow(ecosystems_info),
times = nrow(ds_individuals_t0_not_elongated))) %>%
select(time_point,
day,
video_replicate,
file,
culture_ID,
id,
N_frames,
mean_area)
expect_equal(nrow(ds_individuals_t0_not_elongated) * nrow(ecosystems_info),
nrow(ds_individuals_t0_elongated))#Import t1-t4
ds_individuals_t1_to_t4 = NULL
for (time_point_i in time_points_without_t0) {
ds_individuals_t1_to_t4[[time_point_i]] = read.csv(here("2_data",
"individuals_13_threshold",
paste0("t",
time_point_i,
".csv"))) %>%
mutate(time_point = as.numeric(str_extract(time_point, "\\d+")),
day = time_point_day$day[time_point_day$time_point == time_point_i],
file = as.numeric(str_extract(file, "\\d+")),
video_replicate = ceiling(file/n_cultures)) #Until 110 video replicate = 1, then 2
}
ds_individuals_t1_to_t4 = ds_individuals_t1_to_t4 %>%
bind_rows() %>%
select(time_point,
day,
video_replicate,
file,
culture_ID,
id,
N_frames,
mean_area)# Bind t0 with t1-t4
ds_individuals = rbind(ds_individuals_t0_elongated,
ds_individuals_t1_to_t4) %>%
left_join(ecosystems_info,
by = "culture_ID") # Rename and select columns
ds_individuals = ds_individuals %>%
rename(ecosystem_size = patch_size,
ecosystem_size_volume = patch_size_volume) %>%
select(
disturbance,
disturbance_volume,
time_point,
day,
video_replicate,
culture_ID,
system_nr,
file,
eco_metaeco_type,
ecosystem_size,
ecosystem_size_volume,
metaecosystem,
metaecosystem_type,
mean_area,
N_frames
) %>%
rename(ecosystem_size_ml = ecosystem_size_volume,
ecosystem_type = eco_metaeco_type,
body_area_µm2 = mean_area)# Rename and reorder levels
ds_individuals <- ds_individuals %>%
mutate(ecosystem_type = case_when(ecosystem_type == "S" ~ "Small unconnected",
ecosystem_type == "M" ~ "Medium unconnected",
ecosystem_type == "L" ~ "Large unconnected",
ecosystem_type == "S (S_S)" ~ "Small connected to small",
ecosystem_type == "S (S_L)" ~ "Small connected to large",
ecosystem_type == "M (M_M)" ~ "Medium connected to medium",
ecosystem_type == "L (S_L)" ~ "Large connected to small",
ecosystem_type == "L (L_L)" ~ "Large connected to large",
TRUE ~ ecosystem_type),
ecosystem_type = factor(ecosystem_type,
levels = ecosystem_types_ordered))
ds_individuals <- ds_individuals %>%
mutate(ecosystem_size = case_when(ecosystem_size == "S" ~ "Small",
ecosystem_size == "M" ~ "Medium",
ecosystem_size == "L" ~ "Large",
TRUE ~ ecosystem_type),
ecosystem_size = factor(ecosystem_size,
levels = "Small",
"Medium",
"Large"))
ds_individuals <- ds_individuals %>%
mutate(size_connected_ecosystem = case_when(ecosystem_type == "Small connected to small" ~ "Small",
ecosystem_type == "Small connected to large" ~ "Large",
ecosystem_type == "Medium connected to medium" ~ "Medium",
ecosystem_type == "Large connected to large" ~ "Large",
ecosystem_type == "Large connected to small" ~ "Small",
TRUE ~ NA_character_))# Take off problematic videos
ds_individuals_before_taking_off_videos = ds_individuals
ds_individuals = ds_individuals %>%
filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))
diff = setdiff(ds_individuals_before_taking_off_videos, ds_individuals)
expect_equal(nrow(videos_to_take_off),
nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))# Take off problematic cultures
ds_individuals_before_taking_off_cultures = ds_individuals
ds_individuals = ds_individuals %>%
filter(!culture_ID %in% ecosystems_to_take_off)
expect_equal(setdiff(ds_individuals_before_taking_off_cultures,
ds_individuals) %>%
pull(culture_ID) %>%
unique(),
ecosystems_to_take_off)Patches (ds_ecosystems)
In this dataset (ds_ecosystems) each row represents a
ecosystem at a time point. I use the data from the 40 threshold analysis
for Ble, Cep, Spi and the data from the 13 threshold analysis for all
the other protists (Col, Eup, Lox, Pau, Pca, Spi te, Tet).
# Import & bind t0 datasets.
ds_ecosystems_t0 = read.csv(here("2_data",
"ecosystems_13_threshold",
"t0.csv")) %>%
mutate(time_point = as.numeric(str_extract(time_point, "\\d+")),
day = 0,
video_replicate = file) %>%
select(time_point,
day,
video_replicate,
file,
bioarea_per_volume,
indiv_per_volume)
species_ID_13_threshold_t0 = read.csv(here("2_data",
"species_ID_13_threshold",
paste0("t0.csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_13_threshold_indiv_per_volume))
species_ID_40_threshold_t0 = read.csv(here("2_data",
"species_ID_40_threshold",
paste0("t0.csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_40_threshold_indiv_per_volume))
ds_ecosystems_t0 = ds_ecosystems_t0 %>%
left_join(species_ID_13_threshold_t0,
by = "file") %>%
left_join(species_ID_40_threshold_t0,
by = "file") %>%
mutate(file = as.numeric(str_extract(file, "\\d+")))# Elongate t0 dataset.
ds_ecosystems_t0_elongated <- list()
for (video_i in 1 : n_videos_taken_t0) {
single_video = ds_ecosystems_t0 %>%
filter(file == video_i)
ds_ecosystems_t0_elongated[[video_i]] = ecosystems_info %>%
mutate(time_point = 0,
day = 0,
file = single_video$file,
video_replicate = single_video$video_replicate,
bioarea_per_volume = single_video$bioarea_per_volume,
indiv_per_volume = single_video$indiv_per_volume,
Ble_indiv_per_volume = single_video$Ble_indiv_per_volume,
Cep_indiv_per_volume = single_video$Cep_indiv_per_volume,
Col_indiv_per_volume = single_video$Col_indiv_per_volume,
Eug_indiv_per_volume = single_video$Eug_indiv_per_volume,
Eup_indiv_per_volume = single_video$Eup_indiv_per_volume,
Lox_indiv_per_volume = single_video$Lox_indiv_per_volume,
Pau_indiv_per_volume = single_video$Pau_indiv_per_volume,
Pca_indiv_per_volume = single_video$Pca_indiv_per_volume,
Spi_indiv_per_volume = single_video$Spi_indiv_per_volume,
Spi_te_indiv_per_volume = single_video$Spi_te_indiv_per_volume,
Tet_indiv_per_volume = single_video$Tet_indiv_per_volume)
}
ds_ecosystems_t0_elongated = ds_ecosystems_t0_elongated %>%
bind_rows()# Clean the columns of t0
ds_ecosystems_t0 = ds_ecosystems_t0_elongated %>%
select(file,
time_point,
day,
culture_ID,
video_replicate,
bioarea_per_volume,
indiv_per_volume,
all_of(protist_species_indiv_per_volume))
expect_equal(nrow(ds_ecosystems_t0),
sum(n_videos_taken_t0 * n_cultures))# Import and bind t1-t4
ds_ecosystems_t1_to_t4 = NULL
for (time_point_i in time_points_without_t0) {
species_ID_13_threshold = read.csv(here("2_data",
"species_ID_13_threshold",
paste0("t", time_point_i, ".csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_13_threshold_indiv_per_volume))
species_ID_40_threshold = read.csv(here("2_data",
"species_ID_40_threshold",
paste0("t", time_point_i, ".csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_40_threshold_indiv_per_volume))
ds_ecosystems_t1_to_t4[[time_point_i]] = read.csv(here("2_data",
"ecosystems_13_threshold",
paste0("t", time_point_i, ".csv"))) %>%
arrange(file) %>%
mutate(video_replicate = rep(1 : time_point_day$video_replicates[time_point_i+1],
each = n_cultures),
day = time_point_day$day[time_point_day$time_point == time_point_i]) %>%
select(file,
time_point,
day,
video_replicate,
file,
culture_ID,
bioarea_per_volume,
indiv_per_volume)
ds_ecosystems_t1_to_t4[[time_point_i]] = ds_ecosystems_t1_to_t4[[time_point_i]] %>%
left_join(species_ID_13_threshold,
by = "file") %>%
left_join(species_ID_40_threshold,
by = "file")
}
ds_ecosystems_t1_to_t4 = ds_ecosystems_t1_to_t4 %>%
bind_rows()# Bind t0 with t1-t4
ds_ecosystems = rbind(ds_ecosystems_t0,
ds_ecosystems_t1_to_t4) %>%
left_join(ecosystems_info,
by = "culture_ID")
expect_equal(nrow(ds_ecosystems),
sum(sum(time_point_day$video_replicates) * n_cultures))# Reorder and rename columns
ds_ecosystems = ds_ecosystems %>%
rename(ecosystem_size = patch_size,
ecosystem_size_ml = patch_size_volume) %>%
select(file,
time_point,
day,
disturbance,
culture_ID,
system_nr,
eco_metaeco_type,
ecosystem_size,
ecosystem_size_ml,
metaecosystem,
metaecosystem_type,
video_replicate,
bioarea_per_volume,
indiv_per_volume,
all_of(protist_species_indiv_per_volume)) %>%
rename(bioarea_µm2_per_μL = bioarea_per_volume) %>%
rename_all( ~ gsub("volume", "μL", .))# Rename and reorder levels
ds_ecosystems <- ds_ecosystems %>%
mutate(ecosystem_size = case_when(ecosystem_size == "S" ~ "Small",
ecosystem_size == "M" ~ "Medium",
ecosystem_size == "L" ~ "Large",
TRUE ~ ecosystem_size),
connection = case_when(eco_metaeco_type == "S" ~ "unconnected",
eco_metaeco_type == "M" ~ "unconnected",
eco_metaeco_type == "L" ~ "unconnected",
eco_metaeco_type == "S (S_S)" ~ "connected to small",
eco_metaeco_type == "S (S_L)" ~ "connected to large",
eco_metaeco_type == "M (M_M)" ~ "connected to medium",
eco_metaeco_type == "L (S_L)" ~ "connected to small",
eco_metaeco_type == "L (L_L)" ~ "connected to large"),
ecosystem_type = paste(ecosystem_size, connection),
metaecosystem_type = case_when(metaecosystem_type == "S_S" ~ "Small-Small",
metaecosystem_type == "M_M" ~ "Medium-Medium",
metaecosystem_type == "L_L" ~ "Large-Large",
metaecosystem_type == "S_L" ~ "Small-Large",
TRUE ~ metaecosystem_type),
time_point = as.numeric(str_extract(time_point, "\\d+")),
file = as.numeric(str_extract(file, "\\d+")))# Change units of measurments to ml
ds_ecosystems = ds_ecosystems %>%
mutate(bioarea_µm2_per_ml = bioarea_µm2_per_μL * 10^3,
bioarea_mm2_per_ml = bioarea_µm2_per_ml * 10^(-6),
Ble_indiv_per_ml = Ble_indiv_per_μL * 10^3,
Cep_indiv_per_ml = Cep_indiv_per_μL * 10^3,
Col_indiv_per_ml = Col_indiv_per_μL * 10^3,
Eug_indiv_per_ml = Eug_indiv_per_μL * 10^3,
Eup_indiv_per_ml = Eup_indiv_per_μL * 10^3,
Lox_indiv_per_ml = Lox_indiv_per_μL * 10^3,
Pau_indiv_per_ml = Pau_indiv_per_μL * 10^3,
Pca_indiv_per_ml = Pca_indiv_per_μL * 10^3,
Spi_indiv_per_ml = Spi_indiv_per_μL * 10^3,
Spi_te_indiv_per_ml = Spi_te_indiv_per_μL * 10^3,
Tet_indiv_per_ml = Tet_indiv_per_μL * 10^3)# Take off problematic videos
ds_ecosystems_before_taking_off_videos = ds_ecosystems
ds_ecosystems = ds_ecosystems %>%
filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))
diff = setdiff(ds_ecosystems_before_taking_off_videos, ds_ecosystems)
expect_equal(nrow(videos_to_take_off),
nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))# Take off problematic cultures
ds_ecosystems_before_taking_off_cultures = ds_ecosystems
ds_ecosystems = ds_ecosystems %>%
filter(!culture_ID %in% ecosystems_to_take_off)
expect_equal(setdiff(ds_ecosystems_before_taking_off_cultures,
ds_ecosystems) %>%
pull(culture_ID) %>%
unique(),
ecosystems_to_take_off)# Average videos
ds_ecosystems = ds_ecosystems %>%
group_by(across(all_of(columns_ecosystems))) %>%
summarise(across(contains("_per_ml"), mean),
across(contains("_tot"), mean)) %>%
ungroup()
expect_equal(nrow(ds_ecosystems),
(n_cultures - length(ecosystems_to_take_off)) * length(time_points))# Add connection and individuals
ds_ecosystems = ds_ecosystems %>%
mutate(indiv_per_ml = !!rlang::parse_expr(paste(protist_species_indiv_per_ml,
collapse = " + ")))# Calculate total response variable for the whole ecosystem
ds_ecosystems = ds_ecosystems %>%
mutate(bioarea_tot_mm2 = bioarea_mm2_per_ml * ecosystem_size_ml,
indiv_tot = indiv_per_ml * ecosystem_size_ml,
Ble_tot_indiv = Ble_indiv_per_ml * ecosystem_size_ml,
Cep_tot_indiv = Cep_indiv_per_ml * ecosystem_size_ml,
Col_tot_indiv = Col_indiv_per_ml * ecosystem_size_ml,
Eug_tot_indiv = Eug_indiv_per_ml * ecosystem_size_ml,
Eup_tot_indiv = Eup_indiv_per_ml * ecosystem_size_ml,
Lox_tot_indiv = Lox_indiv_per_ml * ecosystem_size_ml,
Pau_tot_indiv = Pau_indiv_per_ml * ecosystem_size_ml,
Pca_tot_indiv = Pca_indiv_per_ml * ecosystem_size_ml,
Spi_tot_indiv = Spi_indiv_per_ml * ecosystem_size_ml,
Spi_te_tot_indiv = Spi_te_indiv_per_ml * ecosystem_size_ml,
Tet_tot_indiv = Tet_indiv_per_ml * ecosystem_size_ml)# Calculate species dominance
ds_ecosystems = ds_ecosystems %>%
mutate(across(.cols = all_of(protist_species_indiv_per_ml),
.fns = list(dominance = ~ (. / indiv_per_ml) * 100),
.names = "{col}_dominance"))
expect_equal(unique(ds_ecosystems$Ble_indiv_per_ml_dominance[ds_ecosystems$indiv_per_ml == 0]), NaN)
if (FALSE %in% unique((ds_ecosystems$Ble_indiv_per_ml/ds_ecosystems$indiv_per_ml) *100 == ds_ecosystems$Ble_indiv_per_ml_dominance)) stop()# Calculate alpha diversity (Shannon, Simpson, Inverse Simpson, Evenness)
n_rows_ds_ecosystems_before_calculating_alpha = nrow(ds_ecosystems)
ds_ecosystems = calculate.alpha.diversity()
expect_equal(max(ds_ecosystems$species_richness),
length(protist_species))
expect_equal(nrow(ds_ecosystems),
n_rows_ds_ecosystems_before_calculating_alpha)# Calculate median body size
n_rows_ds_ecosystems_before_median_size = nrow(ds_ecosystems)
ds_median_body_size = ds_individuals %>%
group_by(time_point,
culture_ID,
file) %>%
summarise(median_body_area_µm2 = median(body_area_µm2)) %>%
group_by(time_point,
culture_ID) %>%
summarise(median_body_area_µm2 = mean(median_body_area_µm2))
expect_true(nrow(ds_median_body_size) <= nrow(ds_ecosystems)) #Ds median body size could be less because some cultures might be crashed and not have any individual.
ds_ecosystems_before_full_join = ds_ecosystems
ds_ecosystems = full_join(ds_ecosystems, ds_median_body_size)
expect_equal(nrow(ds_ecosystems),
n_rows_ds_ecosystems_before_median_size)# Calculate auto/heterotrophic ratio
ds_ecosystems = ds_ecosystems %>%
mutate(auto_hetero_ratio = (Eug_indiv_per_ml + Eup_indiv_per_ml) /
(Ble_indiv_per_ml +
Cep_indiv_per_ml +
Col_indiv_per_ml +
Lox_indiv_per_ml +
Pau_indiv_per_ml +
Pca_indiv_per_ml +
Spi_indiv_per_ml +
Spi_te_indiv_per_ml +
Tet_indiv_per_ml))# Add evaporation rates
ds_for_evaporation = read.csv(here("2_data", "water_addition.csv")) %>%
pivot_longer(cols = starts_with("water_add_after_t"),
names_to = "time_point",
values_to = "water_addition_ml") %>%
mutate(time_point = as.double(str_extract(time_point, "\\d+")) + 1)
ds_ecosystems = ds_ecosystems %>%
left_join(ds_for_evaporation)Patch effect sizes (ds_ecosystems_effect_size)
In this dataset (ds_ecosystems_effect_size) each row
represents a treatment at a time point. It contains the effect size of
the connection of a ecosystem (connected vs unconnected).
# Calculate the mean & sd of response variables for each treatment/control at each time point
ds_ecosystems_effect_size = NULL
variable_nr = 0
for (variable_i in variables_ecosystems) {
variable_nr = variable_nr + 1
ds_ecosystems_effect_size[[variable_nr]] = ds_ecosystems %>%
filter(time_point >= 1,
!is.na(!!sym(variable_i))) %>%
group_by(across(all_of(columns_ecosystems[columns_ecosystems != "culture_ID" &
columns_ecosystems != "system_nr"]))) %>%
summarise(across(all_of(variable_i),
list(mean = mean,
sd = sd)),
sample_size = n()) %>%
rename_with( ~ paste0(variable_i, "_sample_size"),
matches("sample_size"))
}
ds_ecosystems_effect_size <- reduce(ds_ecosystems_effect_size,
full_join,
by = columns_ecosystems[columns_ecosystems != "culture_ID" & columns_ecosystems != "system_nr"])
expect_equal(nrow(ds_ecosystems_effect_size),
n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)# Calculate the effect size (Hedge's d) for each treatment at each time point
for (variable_i in variables_ecosystems) {
ds_ecosystems_effect_size <- ds_ecosystems_effect_size %>%
mutate(!!paste0(variable_i, "_d") := NA,
!!paste0(variable_i, "_d_upper") := NA,
!!paste0(variable_i, "_d_lower") := NA)
}
row_i = 0
for (treatment_selected in treatments_and_controls$treatment) {
for (time_point_selected in time_points) {
row_i = row_i + 1
control_input = treatments_and_controls$control[treatments_and_controls$treatment == treatment_selected]
treatment_row = ds_ecosystems_effect_size %>%
filter(ecosystem_type == treatment_selected,
time_point == time_point_selected)
control_row = ds_ecosystems_effect_size %>%
filter(ecosystem_type == control_input,
time_point == time_point_selected)
for (response_variable in variables_ecosystems) {
hedges_d = calculate.hedges_d(treatment_row[[paste0(response_variable, "_mean")]],
treatment_row[[paste0(response_variable, "_sd")]],
treatment_row[[paste0(response_variable, "_sample_size")]],
control_row[[paste0(response_variable, "_mean")]],
control_row[[paste0(response_variable, "_sd")]],
control_row[[paste0(response_variable, "_sample_size")]])
ds_ecosystems_effect_size[[paste0(response_variable, "_d")]][
ds_ecosystems_effect_size$ecosystem_type == treatment_selected &
ds_ecosystems_effect_size$time_point == time_point_selected] =
hedges_d$d
ds_ecosystems_effect_size[[paste0(response_variable, "_d_upper")]][
ds_ecosystems_effect_size$ecosystem_type == treatment_selected &
ds_ecosystems_effect_size$time_point == time_point_selected] =
hedges_d$upper_CI
ds_ecosystems_effect_size[[paste0(response_variable, "_d_lower")]][
ds_ecosystems_effect_size$ecosystem_type == treatment_selected &
ds_ecosystems_effect_size$time_point == time_point_selected] =
hedges_d$lower_CI
}
}
}
expect_equal(nrow(ds_ecosystems_effect_size),
n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)Meta-ecosystems (ds_metaecosystems)
In this dataset (ds_metaecosystems) each row represents
a meta-ecosystem or a two-ecosystem unconnected system at a time
point.
# --- Find the IDs of unconnected ecosystems --- #
ID_unconnected_S_low = ds_ecosystems %>%
filter(ecosystem_type == "Small unconnected",
disturbance == "low") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_M_low = ds_ecosystems %>%
filter(ecosystem_type == "Medium unconnected",
disturbance == "low") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_L_low = ds_ecosystems %>%
filter(ecosystem_type == "Large unconnected",
disturbance == "low") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_S_high = ds_ecosystems %>%
filter(ecosystem_type == "Small unconnected",
disturbance == "high") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_M_high = ds_ecosystems %>%
filter(ecosystem_type == "Medium unconnected",
disturbance == "high") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_L_high = ds_ecosystems %>%
filter(ecosystem_type == "Large unconnected",
disturbance == "high") %>%
pull(culture_ID) %>%
unique()# --- Find combinations of ecosystems to create unconnected meta-ecosystems --- #
combinations_S_and_L_low = crossing(ID_unconnected_S_low,
ID_unconnected_L_low) %>%
mutate(disturbance = "low",
metaecosystem_type = "Small-Large",
connection = "unconnected") %>%
rename(ID_first_ecosystem = ID_unconnected_S_low,
ID_second_ecosystem = ID_unconnected_L_low) %>%
select(disturbance,
metaecosystem_type,
connection,
ID_first_ecosystem,
ID_second_ecosystem)
combinations_S_and_L_high = crossing(ID_unconnected_S_high,
ID_unconnected_L_high) %>%
mutate(disturbance = "high",
metaecosystem_type = "Small-Large",
connection = "unconnected") %>%
rename(ID_first_ecosystem = ID_unconnected_S_high,
ID_second_ecosystem = ID_unconnected_L_high) %>%
select(disturbance,
metaecosystem_type,
connection,
ID_first_ecosystem,
ID_second_ecosystem)
combinations_M_and_M_low = combinat::combn(ID_unconnected_M_low,
m = 2) %>%
t() %>%
as.data.frame() %>%
rename(ID_first_ecosystem = V1,
ID_second_ecosystem = V2) %>%
mutate(disturbance = "low",
metaecosystem_type = "Medium-Medium",
connection = "unconnected") %>%
select(disturbance,
metaecosystem_type,
connection,
ID_first_ecosystem,
ID_second_ecosystem)
combinations_M_and_M_high = combinat::combn(ID_unconnected_M_high,
m = 2) %>%
t() %>%
as.data.frame() %>%
rename(ID_first_ecosystem = V1,
ID_second_ecosystem = V2) %>%
mutate(disturbance = "high",
metaecosystem_type = "Medium-Medium",
connection = "unconnected") %>%
select(disturbance,
metaecosystem_type,
connection,
ID_first_ecosystem,
ID_second_ecosystem)# --- Bind ecosystem combinations --- #
combinations_unconnected_metaeco = rbind(combinations_S_and_L_low,
combinations_S_and_L_high,
combinations_M_and_M_low,
combinations_M_and_M_high) %>%
mutate(system_nr = 1001:(1000 + nrow(.))) %>%
select(system_nr,
disturbance,
metaecosystem_type,
connection,
ID_first_ecosystem,
ID_second_ecosystem)# --- Find combinations of ecosystems to create connected meta-ecosystems --- #
combinations_connected_metaeco = ds_ecosystems %>%
filter(time_point == 0,
metaecosystem == "yes") %>%
select(system_nr,
disturbance,
metaecosystem_type,
culture_ID) %>%
group_by(system_nr,
disturbance,
metaecosystem_type) %>%
summarise(ID_first_ecosystem = (mean(culture_ID) - 0.5),
ID_second_ecosystem = (mean(culture_ID) + 0.5)) %>%
mutate(connection = "connected") %>%
as.data.frame()# --- Bind combinations of ecosystems to create unconnected and connected meta-ecosystems --- #
ecosystem_combinations = rbind(combinations_unconnected_metaeco,
combinations_connected_metaeco) %>%
mutate(ecosystems_combined = paste0(ID_first_ecosystem, "|", ID_second_ecosystem))
n_ecosystems_combinations = nrow(ecosystem_combinations)# --- Create sets for SL unconnected, where in each set a small and a large ecosystems are paired differently --- #
#I keep the small ecosystems on the same order and perform permutations on large ecosystems
SL_unconnected_sys_sets <- vector("list",
length(disturbance_levels))
for (disturbance_i in 1:length(disturbance_levels)) {
ID_small_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_levels[disturbance_i],
ecosystem_type == "Small unconnected") %>%
pull(culture_ID) %>%
unique()
ID_large_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_levels[disturbance_i],
ecosystem_type == "Large unconnected") %>%
pull(culture_ID) %>%
unique()
#Force small and large ecosystems vectors to have the same length
length_difference <- length(ID_small_ecosystems) - length(ID_large_ecosystems)
if (length_difference > 0) {
ID_large_ecosystems = c(ID_large_ecosystems,
rep("Patch taken off",
times = abs(length(ID_small_ecosystems) -
length(ID_large_ecosystems))))
} else if (length_difference < 0) {
ID_small_ecosystems = c(ID_small_ecosystems,
rep("Patch taken off",
times = abs(length(ID_large_ecosystems) -
length(ID_small_ecosystems))))
}
# Create dataframe
permutations_large = permn(ID_large_ecosystems)
SL_unconnected_sys_sets[[disturbance_i]] = data.frame(disturbance = disturbance_levels[disturbance_i],
metaecosystem_type = "Small-Large",
connection = "unconnected",
ID_first_ecosystem = rep(ID_small_ecosystems, times = length(permutations_large)),
ID_second_ecosystem = unlist(permutations_large),
set = rep(1 : length(permutations_large),
each = length(ID_small_ecosystems)))
expect_equal(nrow(SL_unconnected_sys_sets[[disturbance_i]]),
length(ID_small_ecosystems) * length(permutations_large))
SL_unconnected_sys_sets[[disturbance_i]] = SL_unconnected_sys_sets[[disturbance_i]] %>%
filter(!ID_first_ecosystem == "Patch taken off",
!ID_second_ecosystem == "Patch taken off") %>%
mutate(ID_first_ecosystem = as.double(ID_first_ecosystem),
ID_second_ecosystem = as.double(ID_second_ecosystem)) %>%
full_join(ecosystem_combinations %>%
filter(disturbance == disturbance_levels[disturbance_i],
metaecosystem_type == "Small-Large",
connection == "unconnected")) #Add system_nr & ecosystems_combined
}
SL_unconnected_sys_sets_before_binding = SL_unconnected_sys_sets
SL_unconnected_sys_sets = SL_unconnected_sys_sets %>%
bind_rows()expect_equal(nrow(SL_unconnected_sys_sets),
nrow(SL_unconnected_sys_sets_before_binding[[1]]) + nrow(SL_unconnected_sys_sets_before_binding[[2]]))
expect_equal(length(SL_unconnected_sys_sets %>%
pull(system_nr) %>%
unique()),
length(ecosystem_combinations %>%
filter(metaecosystem_type == "Small-Large",
connection == "unconnected") %>%
pull(system_nr) %>%
unique()))# --- Create sets for MM unconnected, where in each set two different medium ecosystems are paired--- #
#To do so, I ...
#Initialise MM_unconnected_sets. Assign 10^4 rows to each matrix so that we have enough rows not to run out of them when we try to assign values to them. Assign 4 columns which will include culture_ID of the first system, second culture_ID of the fist system, culture_ID of the second system, and second culture_ID of the second system.
MM_unconnected_sets = NULL
for(disturbance_i in 1:length(disturbance_levels)){
MM_unconnected_sets[[disturbance_i]] <- matrix(nrow = 10 ^ 4,
ncol = 4)
}
for (disturbance_i in 1:length(disturbance_levels)) {
ID_medium_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_levels[disturbance_i],
ecosystem_type == "Medium unconnected") %>%
pull(culture_ID) %>%
unique()
MM_unconnected_systems = combn(ID_medium_ecosystems,
2) %>%
t()
matrix_row = 0
for (first_system_i in 1:nrow(MM_unconnected_systems)) {
#Find culture IDs of the first system (what's the first system?)
first_system = MM_unconnected_systems[first_system_i, ]
for (second_system_i in 1:nrow(MM_unconnected_systems)) {
#Find culture IDs of the second system (what's the second system?)
second_system = MM_unconnected_systems[second_system_i, ]
shared_elements_among_systems = intersect(first_system,
second_system)
if (length(shared_elements_among_systems) == 0) {
matrix_row = matrix_row + 1
#Make first and second system into a set
MM_unconnected_sets[[disturbance_i]][matrix_row,] = c(first_system,
second_system)
print(MM_unconnected_sets[[disturbance_i]][matrix_row,])
}
}
}
#Tidy the dataset with all the ecosystem combinations
MM_unconnected_sets[[disturbance_i]] = MM_unconnected_sets[[disturbance_i]] %>%
as.data.frame() %>%
drop_na()
expect_equal(MM_unconnected_sets[[disturbance_i]] %>%
filter(V1 == V2 | V1 == V3 | V1 == V4 | V2 == V3 | V2 == V4 | V3 == V4) %>%
nrow(),
0)
#Reorder the dataset with all the ecosystem combinations
MM_unconnected_sets_reordered = data.frame(ID_first_ecosystem = NA,
ID_second_ecosystem = NA,
set = NA)
for (set_input in 1:nrow(MM_unconnected_sets[[disturbance_i]])) {
MM_unconnected_sets_reordered = MM_unconnected_sets_reordered %>%
add_row(ID_first_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 1],
ID_second_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 2],
set = set_input) %>%
add_row(ID_first_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 3],
ID_second_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 4],
set = set_input)
}
#Add to a list
MM_unconnected_sets[[disturbance_i]] = MM_unconnected_sets_reordered %>%
drop_na() %>%
mutate(disturbance = disturbance_levels[disturbance_i],
metaecosystem_type = "Medium-Medium",
connection = "unconnected")
#Add system nr
ID_combinations_MM_unconnected = ecosystem_combinations %>%
filter(disturbance == disturbance_levels[disturbance_i],
metaecosystem_type == "Medium-Medium",
connection == "unconnected")
MM_unconnected_sets[[disturbance_i]] = full_join(MM_unconnected_sets[[disturbance_i]],
ID_combinations_MM_unconnected)
}## [1] 6 7 8 9
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## [1] 64 65 62 63#Bind all sets of MM unconnected
MM_unconnected_sets = MM_unconnected_sets %>%
bind_rows()expect_equal(length(MM_unconnected_sets %>%
pull(system_nr) %>%
unique()),
length(ecosystem_combinations %>%
filter(metaecosystem_type == "Medium-Medium",
connection == "unconnected") %>%
pull(system_nr) %>%
unique()))# --- Bind SL and MM unconnected systems --- #
unconnected_combinations_sets = rbind(SL_unconnected_sys_sets,
MM_unconnected_sets) %>%
select(disturbance,
metaecosystem_type,
connection,
set,
system_nr,
ID_first_ecosystem,
ID_second_ecosystem)Each row is a meta-ecosystem.
It contains also “fake” meta-ecosystems which I created from unconnected ecosystems (
metaecosystem type = Small-Large unconnected&metaecosystem type = Medium-Medium unconnected).Warning appear after the following code, as:
- alpha diversity is computed for a culture that is totally crashed, so it has not meaning.
- beta diversity is computed between a culture that is still alive and one that is totally crashed. Because one of the cultures is totally crashed, the Bray-Curtis index is 1.
# --- Compute meta-ecosystems for each time point --- #
ds_metaecosystems = NULL
row_i = 0
for (combination_i in 1:n_ecosystems_combinations) {
for (time_point_selected in time_points) {
row_i = row_i + 1
current_day = sampling_days[time_point_selected + 1]
current_system_nr = ecosystem_combinations[combination_i, ]$system_nr
current_combination = ecosystem_combinations[combination_i, ]$ecosystems_combined
current_disturbance = ecosystem_combinations[combination_i, ]$disturbance
current_metaeco_type = ecosystem_combinations[combination_i, ]$metaecosystem_type
current_connection = ecosystem_combinations[combination_i, ]$connection
current_IDs = c(ecosystem_combinations[combination_i, ]$ID_first_ecosystem,
ecosystem_combinations[combination_i, ]$ID_second_ecosystem)
if (current_system_nr %in% metaecosystems_to_take_off)
next
if (current_IDs[1] == current_IDs[2])
next
species_vector_two_ecosystems = ds_ecosystems %>%
filter(time_point == time_point_selected,
culture_ID %in% current_IDs) %>%
ungroup() %>%
select(all_of(protist_species_indiv_per_ml))
absence_presence_two_ecosystems <-
ifelse(species_vector_two_ecosystems > 0, 1, 0)
#Alpha diversity: Shannon (mean between the two ecosystems)
shannon_ecosystem_1 = diversity(species_vector_two_ecosystems[1, ], index = "shannon")
shannon_ecosystem_2 = diversity(species_vector_two_ecosystems[2, ], index = "shannon")
shannon_value = (shannon_ecosystem_1 + shannon_ecosystem_2) / 2
#Alpha diversity: Species richness (mean between the two ecosystems)
richness_ecosystem_1 = specnumber(species_vector_two_ecosystems[1, ])
richness_ecosystem_2 = specnumber(species_vector_two_ecosystems[2, ])
mean_richness_value = (richness_ecosystem_1 + richness_ecosystem_2) / 2
#Beta diversity: Jaccard
jaccard_index_value = vegdist(species_vector_two_ecosystems,
method = "jaccard") %>%
as.numeric()
#Beta diversity: Bray Curtis
bray_curtis_value = vegdist(species_vector_two_ecosystems,
method = "bray") %>%
as.numeric()
#Beta diversity: partitioning of beta diversity from Sorensen index into turnover (Simpson pair-wise dissimilarity) and nestedness (nestedness-fraction of Sorensen)
betapart_core_object = betapart.core(absence_presence_two_ecosystems)
beta_spatial_turnover_value = beta.pair(betapart_core_object)$beta.sim %>% as.double()
beta_nestedness_value = beta.pair(betapart_core_object)$beta.sne %>% as.double()
beta_total_value = beta.pair(betapart_core_object)$beta.sor %>% as.double()
#Gamma diversity: Meta-ecosystem richness
metaecosystem_richness_value = colSums(species_vector_two_ecosystems) %>%
specnumber()
#Put everything together
ds_metaecosystems[[row_i]] = ds_ecosystems %>%
filter(culture_ID %in% current_IDs,
time_point == time_point_selected) %>%
summarise(total_metaecosystem_bioarea_mm2 = sum(bioarea_tot_mm2),
total_metaecosystem_Ble_indiv = sum(Ble_tot_indiv),
total_metaecosystem_Cep_indiv = sum(Cep_tot_indiv),
total_metaecosystem_Col_indiv = sum(Col_tot_indiv),
total_metaecosystem_Eug_indiv = sum(Eug_tot_indiv),
total_metaecosystem_Eup_indiv = sum(Eup_tot_indiv),
total_metaecosystem_Lox_indiv = sum(Lox_tot_indiv),
total_metaecosystem_Pau_indiv = sum(Pau_tot_indiv),
total_metaecosystem_Pca_indiv = sum(Pca_tot_indiv),
total_metaecosystem_Spi_indiv = sum(Spi_tot_indiv),
total_metaecosystem_Spi_te_indiv = sum(Spi_te_tot_indiv),
total_metaecosystem_Tet_indiv = sum(Tet_tot_indiv),
total_water_addition_ml = sum(water_addition_ml)) %>%
mutate(system_nr = current_system_nr,
ecosystems_combined = current_combination,
metaecosystem_type = current_metaeco_type,
ecosystem_size_symmetry = case_when(metaecosystem_type == "Small-Large" ~ "asymmetric",
metaecosystem_type == "Medium-Medium" ~ "symmetric",
metaecosystem_type == "Small-Small" ~ "symmetric",
metaecosystem_type == "Large-Large" ~ "symmetric"),
connection = current_connection,
disturbance = current_disturbance,
time_point = time_point_selected,
day = current_day,
jaccard_index = jaccard_index_value,
bray_curtis = bray_curtis_value,
beta_spatial_turnover = beta_spatial_turnover_value,
beta_nestedness = beta_nestedness_value,
beta_total = beta_total_value,
metaecosystem_richness = metaecosystem_richness_value,
mean_shannon = shannon_value,
mean_richness = mean_richness_value) %>%
ungroup()
}
}## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"ds_metaecosystems = ds_metaecosystems %>%
bind_rows() %>%
as.data.frame() %>%
select(time_point,
day,
system_nr,
ecosystems_combined,
disturbance,
metaecosystem_type,
ecosystem_size_symmetry,
connection,
mean_shannon,
mean_richness,
jaccard_index,
bray_curtis,
beta_spatial_turnover,
beta_nestedness,
beta_total,
metaecosystem_richness,
total_metaecosystem_bioarea_mm2,
paste0("total_metaecosystem_", protist_species, "_indiv"),
total_water_addition_ml)expect_equal(nrow(ds_metaecosystems),
n_time_points * n_ecosystems_combinations)Filter according to disturbance
Here I’m filtering ecosystems to have only the ones with disturbance low.
ds_ecosystems_both_disturbances = ds_ecosystems
ds_metaecosystems_both_disturbances = ds_metaecosystems#Filter data sets according to the global disturbance
ds_individuals = ds_individuals %>%
filter(disturbance == disturbance_global_selected)
ds_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_global_selected)
ds_ecosystems_effect_size = ds_ecosystems_effect_size %>%
filter(disturbance == disturbance_global_selected)
ds_metaecosystems = ds_metaecosystems %>%
filter(disturbance == disturbance_global_selected)ds_classes = ds_classes %>%
filter(disturbance == disturbance_global_selected)
ds_classes_effect_size = ds_classes_effect_size %>%
filter(disturbance == disturbance_global_selected)Plots & Analysis
All meta-ecosystems
metaecosystem_type_selected = c("Small-Small",
"Large-Large",
"Medium-Medium",
"Small-Large")
connection_selected = c("connected",
"unconnected")Alpha
response_variable_selected = "mean_shannon"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
Beta
response_variable_selected = "bray_curtis"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
Gamma
response_variable_selected = "metaecosystem_richness"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
Biomass
response_variable_selected = "total_metaecosystem_bioarea_mm2"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
SL vs MM
Alpha
response_variable_selected = "mean_shannon"metaecosystem_type_selected = c("Medium-Medium",
"Small-Large")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: SL (connected vs unconnected) and MM (connected vs unconnected).
comparison_type = "all"SL
metaecosystem_type_selected = c("Small-Large")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -8.1 0.002 *** strongΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1001 1010 1012 1018 1024 -11.383343
## 2 1002 1010 1011 1018 1024 -11.328115
## 3 1003 1010 1012 1016 1024 -11.174864
## 4 1003 1010 1014 1016 1022 -10.933920
## 5 1004 1010 1013 1016 1022 -10.933184
## 6 1004 1010 1011 1018 1022 -10.805806
## 7 1001 1010 1014 1018 1022 -10.797472
## 8 1002 1010 1013 1016 1024 -10.548428
## 9 1001 1009 1012 1018 1025 -10.519043
## 10 1002 1009 1011 1018 1025 -10.395574
## 11 1003 1009 1012 1016 1025 -10.240548
## 12 1004 1007 1011 1018 1025 -10.041854
## 13 1005 1009 1011 1018 1022 -9.949156
## 14 1001 1007 1014 1018 1025 -9.882950
## 15 1004 1007 1013 1016 1025 -9.879992
## 16 1003 1007 1014 1016 1025 -9.859963
## 17 1001 1010 1013 1019 1022 -9.818651
## 18 1005 1006 1012 1018 1024 -9.793929
## 19 1005 1009 1012 1018 1021 -9.789922
## 20 1003 1010 1011 1019 1022 -9.755006
## 21 1002 1006 1015 1018 1024 -9.738514
## 22 1003 1007 1011 1019 1025 -9.687114
## 23 1003 1010 1011 1017 1024 -9.643670
## 24 1002 1009 1015 1018 1021 -9.550444
## 25 1002 1009 1013 1016 1025 -9.499003
## 26 1001 1007 1013 1019 1025 -9.485720
## 27 1001 1009 1015 1018 1022 -9.483894
## 28 1003 1006 1012 1019 1025 -9.295254
## 29 1005 1007 1011 1018 1024 -9.286050
## 30 1004 1010 1012 1018 1021 -9.208206
## 31 1001 1010 1013 1017 1024 -9.202064
## 32 1002 1010 1014 1018 1021 -9.166703
## 33 1003 1009 1015 1016 1022 -9.141212
## 34 1001 1007 1015 1018 1024 -9.137349
## 35 1003 1009 1011 1017 1025 -9.118260
## 36 1002 1006 1014 1018 1025 -9.078364
## 37 1005 1009 1013 1016 1022 -9.049262
## 38 1004 1006 1012 1018 1025 -8.961546
## 39 1002 1006 1013 1019 1025 -8.950068
## 40 1004 1010 1012 1016 1023 -8.877905
## 41 1005 1009 1013 1017 1021 -8.873756
## 42 1005 1006 1013 1017 1024 -8.794243
## 43 1001 1008 1012 1019 1025 -8.765010
## 44 1003 1007 1015 1016 1024 -8.763294
## 45 1003 1006 1015 1017 1024 -8.720595
## 46 1003 1009 1015 1017 1021 -8.658542
## 47 1001 1009 1013 1017 1025 -8.647701
## 48 1003 1006 1014 1017 1025 -8.589933
## 49 1002 1008 1011 1019 1025 -8.564721
## 50 1005 1007 1013 1016 1024 -8.482529
## 51 1002 1009 1013 1020 1021 -8.479112
## 52 1003 1009 1012 1020 1021 -8.462213
## 53 1003 1010 1014 1017 1021 -8.448371
## 54 1002 1006 1013 1020 1024 -8.436634
## 55 1003 1010 1012 1019 1021 -8.421830
## 56 1003 1006 1012 1020 1024 -8.346155
## 57 1001 1010 1012 1019 1023 -8.196195
## 58 1002 1010 1013 1019 1021 -8.101075
## 59 1002 1010 1014 1016 1023 -8.081882
## 60 1004 1010 1013 1017 1021 -8.069221
## 61 1004 1008 1012 1016 1025 -8.064654
## 62 1003 1009 1011 1020 1022 -8.019092
## 63 1004 1006 1013 1017 1025 -7.930107
## 64 1002 1008 1014 1016 1025 -7.879461
## 65 1002 1010 1011 1019 1023 -7.678822
## 66 1004 1006 1015 1018 1022 -7.671478
## 67 1001 1009 1013 1020 1022 -7.670189
## 68 1004 1010 1011 1017 1023 -7.544221
## 69 1001 1008 1014 1017 1025 -7.533712
## 70 1005 1006 1014 1018 1022 -7.412862
## 71 1004 1007 1015 1018 1021 -7.391612
## 72 1003 1007 1011 1020 1024 -7.376748
## 73 1001 1010 1014 1017 1023 -7.369967
## 74 1004 1008 1011 1017 1025 -7.349374
## 75 1005 1007 1014 1018 1021 -7.256318
## 76 1005 1009 1012 1016 1023 -7.221756
## 77 1001 1007 1013 1020 1024 -7.162613
## 78 1005 1009 1011 1017 1023 -6.995350
## 79 1003 1006 1015 1019 1022 -6.911660
## 80 1002 1009 1015 1016 1023 -6.905013
## 81 1004 1008 1015 1016 1022 -6.893383
## 82 1004 1007 1015 1016 1023 -6.815311
## 83 1005 1008 1011 1017 1024 -6.674473
## 84 1003 1007 1015 1019 1021 -6.627537
## 85 1005 1008 1012 1016 1024 -6.608582
## 86 1002 1008 1015 1016 1024 -6.598162
## 87 1002 1009 1011 1020 1023 -6.556795
## 88 1001 1008 1015 1019 1022 -6.549127
## 89 1001 1009 1015 1017 1023 -6.497347
## 90 1001 1008 1015 1017 1024 -6.351890
## 91 1002 1008 1011 1020 1024 -6.339936
## 92 1001 1009 1012 1020 1023 -6.327408
## 93 1001 1007 1015 1019 1023 -6.301880
## 94 1002 1008 1015 1019 1021 -6.235505
## 95 1004 1006 1013 1020 1022 -6.187536
## 96 1005 1006 1013 1019 1022 -6.187145
## 97 1003 1006 1014 1020 1022 -6.169508
## 98 1005 1008 1014 1017 1021 -6.148744
## 99 1005 1007 1014 1016 1023 -6.105929
## 100 1004 1008 1015 1017 1021 -6.076797
## 101 1003 1007 1014 1020 1021 -6.068296
## 102 1005 1007 1013 1019 1021 -6.061303
## 103 1002 1006 1015 1019 1023 -6.050462
## 104 1001 1008 1012 1020 1024 -6.019178
## 105 1004 1007 1013 1020 1021 -6.000434
## 106 1005 1008 1014 1016 1022 -5.983552
## 107 1004 1006 1015 1017 1023 -5.974636
## 108 1005 1006 1014 1017 1023 -5.911575
## 109 1002 1008 1014 1020 1021 -5.847354
## 110 1005 1008 1011 1019 1022 -5.714150
## 111 1005 1008 1012 1019 1021 -5.690115
## 112 1002 1006 1014 1020 1023 -5.638152
## 113 1005 1007 1011 1019 1023 -5.620162
## 114 1005 1006 1012 1019 1023 -5.586102
## 115 1004 1008 1012 1020 1021 -5.575066
## 116 1004 1008 1011 1020 1022 -5.555692
## 117 1004 1006 1012 1020 1023 -5.515638
## 118 1004 1007 1011 1020 1023 -5.414948
## 119 1001 1008 1014 1020 1022 -5.183459
## 120 1001 1007 1014 1020 1023 -5.141150
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -3.2 0.022 ** moderateΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1003 1007 1011 1019 1025 -7.523754233
## 2 1001 1008 1012 1019 1025 -7.314805651
## 3 1003 1006 1012 1019 1025 -7.306793129
## 4 1002 1008 1011 1019 1025 -7.166294261
## 5 1001 1007 1013 1019 1025 -7.117128028
## 6 1003 1010 1011 1019 1022 -6.970018830
## 7 1001 1010 1013 1019 1022 -6.852916359
## 8 1002 1006 1013 1019 1025 -6.759631629
## 9 1003 1010 1014 1016 1022 -6.657599460
## 10 1003 1007 1014 1016 1025 -6.352001507
## 11 1001 1010 1014 1018 1022 -6.272371097
## 12 1003 1006 1014 1017 1025 -5.994301035
## 13 1001 1007 1014 1018 1025 -5.954887023
## 14 1001 1010 1012 1018 1024 -5.912371031
## 15 1001 1008 1014 1017 1025 -5.858276956
## 16 1003 1010 1012 1016 1024 -5.837920984
## 17 1003 1010 1012 1019 1021 -5.766613051
## 18 1002 1008 1014 1016 1025 -5.687159431
## 19 1001 1010 1012 1019 1023 -5.663397934
## 20 1003 1010 1011 1017 1024 -5.600466330
## 21 1003 1010 1014 1017 1021 -5.457235261
## 22 1002 1010 1011 1018 1024 -5.364914131
## 23 1002 1006 1014 1018 1025 -5.242368043
## 24 1002 1010 1013 1019 1021 -5.018674880
## 25 1002 1010 1011 1019 1023 -4.981483849
## 26 1001 1010 1013 1017 1024 -4.767363051
## 27 1004 1007 1011 1018 1025 -4.731624383
## 28 1004 1008 1011 1017 1025 -4.636186795
## 29 1001 1010 1014 1017 1023 -4.632341256
## 30 1004 1008 1012 1016 1025 -4.617155038
## 31 1001 1008 1015 1019 1022 -4.605019421
## 32 1003 1006 1015 1019 1022 -4.583597599
## 33 1004 1007 1013 1016 1025 -4.471763813
## 34 1002 1008 1015 1019 1021 -4.445821830
## 35 1005 1006 1012 1018 1024 -4.305088431
## 36 1002 1010 1013 1016 1024 -4.298200774
## 37 1002 1010 1014 1018 1021 -4.287379506
## 38 1003 1006 1015 1017 1024 -4.240755665
## 39 1004 1010 1011 1018 1022 -4.227095947
## 40 1004 1010 1013 1016 1022 -4.194233151
## 41 1003 1007 1015 1019 1021 -4.178771461
## 42 1005 1006 1013 1017 1024 -4.127548336
## 43 1005 1008 1014 1017 1021 -3.937311595
## 44 1005 1008 1012 1019 1021 -3.934527132
## 45 1002 1006 1015 1019 1023 -3.921767818
## 46 1001 1007 1015 1019 1023 -3.888180274
## 47 1004 1006 1012 1018 1025 -3.875292259
## 48 1002 1006 1015 1018 1024 -3.872512881
## 49 1005 1007 1011 1018 1024 -3.871264744
## 50 1005 1008 1011 1019 1022 -3.818678888
## 51 1003 1007 1015 1016 1024 -3.812205658
## 52 1004 1006 1013 1017 1025 -3.801729797
## 53 1001 1007 1015 1018 1024 -3.724868006
## 54 1005 1006 1013 1019 1022 -3.656544618
## 55 1002 1010 1014 1016 1023 -3.613144472
## 56 1005 1008 1011 1017 1024 -3.538379417
## 57 1004 1010 1011 1017 1023 -3.529986617
## 58 1005 1006 1012 1019 1023 -3.484351801
## 59 1004 1010 1013 1017 1021 -3.389801416
## 60 1004 1010 1012 1016 1023 -3.236074575
## 61 1003 1009 1012 1016 1025 -3.212890387
## 62 1005 1007 1013 1019 1021 -3.170933208
## 63 1003 1009 1011 1017 1025 -3.103757385
## 64 1005 1006 1014 1018 1022 -3.099894911
## 65 1005 1008 1014 1016 1022 -3.088592856
## 66 1005 1006 1014 1017 1023 -3.081451108
## 67 1004 1010 1012 1018 1021 -3.080072868
## 68 1005 1007 1011 1019 1023 -3.043525709
## 69 1002 1008 1014 1020 1021 -2.985554092
## 70 1001 1008 1015 1017 1024 -2.978066786
## 71 1005 1008 1012 1016 1024 -2.886891291
## 72 1002 1008 1015 1016 1024 -2.848785200
## 73 1003 1006 1012 1020 1024 -2.826433451
## 74 1005 1007 1013 1016 1024 -2.796105927
## 75 1001 1009 1012 1018 1025 -2.707071018
## 76 1004 1008 1015 1017 1021 -2.655918008
## 77 1003 1007 1011 1020 1024 -2.626371198
## 78 1005 1007 1014 1018 1021 -2.595215047
## 79 1004 1008 1015 1016 1022 -2.578701618
## 80 1002 1008 1011 1020 1024 -2.450200597
## 81 1003 1007 1014 1020 1021 -2.420175355
## 82 1002 1006 1013 1020 1024 -2.368141681
## 83 1002 1009 1011 1018 1025 -2.356191205
## 84 1001 1008 1014 1020 1022 -2.298672528
## 85 1001 1009 1013 1017 1025 -2.243702168
## 86 1003 1006 1014 1020 1022 -2.228850876
## 87 1002 1009 1013 1016 1025 -2.043636792
## 88 1001 1008 1012 1020 1024 -2.014843410
## 89 1004 1007 1015 1016 1023 -2.013007089
## 90 1005 1007 1014 1016 1023 -1.964213652
## 91 1004 1006 1015 1017 1023 -1.919721687
## 92 1002 1006 1014 1020 1023 -1.905534227
## 93 1004 1007 1015 1018 1021 -1.878713520
## 94 1003 1009 1015 1017 1021 -1.843772349
## 95 1001 1007 1013 1020 1024 -1.801784665
## 96 1001 1007 1014 1020 1023 -1.776539218
## 97 1004 1006 1015 1018 1022 -1.651922493
## 98 1004 1008 1012 1020 1021 -1.547329922
## 99 1005 1009 1013 1017 1021 -1.525336622
## 100 1003 1009 1015 1016 1022 -1.432901114
## 101 1004 1008 1011 1020 1022 -1.344454099
## 102 1004 1007 1011 1020 1023 -1.143843444
## 103 1005 1009 1011 1018 1022 -1.008570885
## 104 1004 1007 1013 1020 1021 -0.928139209
## 105 1005 1009 1012 1018 1021 -0.913460220
## 106 1004 1006 1012 1020 1023 -0.780166126
## 107 1005 1009 1011 1017 1023 -0.621169076
## 108 1005 1009 1013 1016 1022 -0.533024758
## 109 1001 1009 1015 1018 1022 -0.526565765
## 110 1002 1009 1015 1018 1021 -0.495332141
## 111 1004 1006 1013 1020 1022 -0.414910456
## 112 1001 1009 1015 1017 1023 -0.290689677
## 113 1003 1009 1012 1020 1021 -0.218960891
## 114 1002 1009 1015 1016 1023 -0.145302006
## 115 1005 1009 1012 1016 1023 0.001398768
## 116 1003 1009 1011 1020 1022 0.107520674
## 117 1002 1009 1013 1020 1021 0.446712002
## 118 1002 1009 1011 1020 1023 0.526843011
## 119 1001 1009 1012 1020 1023 0.639881348
## 120 1001 1009 1013 1020 1022 0.877017195MM
metaecosystem_type_selected = c("Medium-Medium")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.4 0.167 noneΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1051 1054 -4.2568461
## 2 1054 1051 -4.2568461
## 3 1048 1054 -3.1415617
## 4 1054 1048 -3.1415617
## 5 1047 1051 -2.8437776
## 6 1051 1047 -2.8437776
## 7 1048 1050 -2.5739244
## 8 1050 1048 -2.5739244
## 9 1050 1055 -2.2893076
## 10 1055 1050 -2.2893076
## 11 1047 1055 -1.2693892
## 12 1055 1047 -1.2693892
## 13 1052 1053 0.3690701
## 14 1053 1052 0.3690701
## 15 1046 1053 0.4150055
## 16 1053 1046 0.4150055
## 17 1049 1053 0.8758528
## 18 1053 1049 0.8758528
## 19 1046 1054 0.9534051
## 20 1054 1046 0.9534051
## 21 1049 1051 1.5480140
## 22 1051 1049 1.5480140
## 23 1048 1052 1.6813026
## 24 1052 1048 1.6813026
## 25 1047 1052 1.7657519
## 26 1052 1047 1.7657519
## 27 1046 1055 1.8032639
## 28 1055 1046 1.8032639
## 29 1049 1050 1.8748924
## 30 1050 1049 1.8748924
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.638 noneΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1049 1053 1.362147
## 2 1053 1049 1.362147
## 3 1048 1050 1.424910
## 4 1050 1048 1.424910
## 5 1048 1054 1.433922
## 6 1054 1048 1.433922
## 7 1049 1051 1.669277
## 8 1051 1049 1.669277
## 9 1051 1054 1.683158
## 10 1054 1051 1.683158
## 11 1046 1053 1.727628
## 12 1053 1046 1.727628
## 13 1047 1051 1.739765
## 14 1051 1047 1.739765
## 15 1050 1055 1.778962
## 16 1055 1050 1.778962
## 17 1049 1050 1.819666
## 18 1050 1049 1.819666
## 19 1047 1055 1.829126
## 20 1055 1047 1.829126
## 21 1046 1055 1.848900
## 22 1055 1046 1.848900
## 23 1048 1052 1.902618
## 24 1052 1048 1.902618
## 25 1052 1053 1.953227
## 26 1053 1052 1.953227
## 27 1046 1054 1.966968
## 28 1054 1046 1.966968
## 29 1047 1052 1.995053
## 30 1052 1047 1.995053Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: SL (connected vs unconnected) and MM (connected vs unconnected).
Beta
response_variable_selected = "bray_curtis"metaecosystem_type_selected = c("Medium-Medium",
"Small-Large")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
SL
metaecosystem_type_selected = c("Small-Large")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: optimx (L-BFGS-B)"
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## [1] "Model successfully fitted with optimizer: optimx (L-BFGS-B)"
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: Nelder_Mead "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -13.5 < 0.001 **** very strongΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1005 1007 1011 1018 1024 -19.868901
## 2 1005 1008 1011 1017 1024 -18.810536
## 3 1003 1007 1011 1020 1024 -18.800952
## 4 1005 1006 1012 1018 1024 -18.531762
## 5 1005 1006 1013 1017 1024 -18.156957
## 6 1002 1008 1011 1020 1024 -17.928143
## 7 1002 1010 1011 1018 1024 -17.776999
## 8 1003 1010 1011 1017 1024 -17.468673
## 9 1002 1006 1013 1020 1024 -17.285922
## 10 1005 1007 1013 1016 1024 -17.262810
## 11 1003 1006 1012 1020 1024 -17.077173
## 12 1005 1008 1012 1016 1024 -17.060543
## 13 1001 1007 1013 1020 1024 -16.775372
## 14 1002 1006 1015 1018 1024 -16.694557
## 15 1001 1007 1015 1018 1024 -16.677117
## 16 1005 1007 1011 1019 1023 -16.587387
## 17 1005 1007 1013 1019 1021 -16.352645
## 18 1003 1007 1015 1016 1024 -16.268515
## 19 1001 1008 1012 1020 1024 -16.211178
## 20 1005 1006 1012 1019 1023 -16.107655
## 21 1005 1008 1012 1019 1021 -16.014871
## 22 1001 1010 1012 1018 1024 -15.983813
## 23 1003 1006 1015 1017 1024 -15.953119
## 24 1003 1010 1012 1016 1024 -15.706239
## 25 1002 1008 1015 1016 1024 -15.612957
## 26 1005 1008 1011 1019 1022 -15.539390
## 27 1002 1010 1013 1016 1024 -15.391378
## 28 1002 1010 1011 1019 1023 -15.388479
## 29 1001 1010 1013 1017 1024 -15.344149
## 30 1002 1006 1015 1019 1023 -15.330564
## 31 1005 1006 1013 1019 1022 -15.273635
## 32 1001 1008 1015 1017 1024 -15.247117
## 33 1005 1009 1011 1018 1022 -15.172346
## 34 1003 1007 1015 1019 1021 -15.115422
## 35 1002 1008 1015 1019 1021 -14.982364
## 36 1005 1009 1011 1017 1023 -14.946169
## 37 1002 1010 1013 1019 1021 -14.921095
## 38 1005 1009 1012 1018 1021 -14.891439
## 39 1003 1010 1012 1019 1021 -14.842129
## 40 1003 1007 1011 1019 1025 -14.789295
## 41 1005 1009 1013 1017 1021 -14.778419
## 42 1003 1010 1011 1019 1022 -14.690961
## 43 1002 1009 1011 1018 1025 -14.653380
## 44 1002 1008 1011 1019 1025 -14.531017
## 45 1003 1009 1011 1020 1022 -14.510780
## 46 1002 1009 1011 1020 1023 -14.451107
## 47 1002 1006 1013 1019 1025 -14.444938
## 48 1002 1009 1013 1020 1021 -14.323230
## 49 1001 1009 1013 1020 1022 -14.066693
## 50 1005 1009 1013 1016 1022 -14.016928
## 51 1003 1009 1012 1020 1021 -14.005396
## 52 1002 1009 1015 1018 1021 -14.000163
## 53 1003 1009 1011 1017 1025 -13.980456
## 54 1001 1009 1012 1018 1025 -13.931415
## 55 1003 1006 1015 1019 1022 -13.899859
## 56 1005 1009 1012 1016 1023 -13.897050
## 57 1001 1009 1015 1018 1022 -13.853938
## 58 1001 1007 1013 1019 1025 -13.581925
## 59 1001 1009 1012 1020 1023 -13.534560
## 60 1001 1007 1015 1019 1023 -13.507945
## 61 1003 1009 1015 1017 1021 -13.465717
## 62 1003 1006 1012 1019 1025 -13.453673
## 63 1002 1009 1013 1016 1025 -13.363448
## 64 1003 1009 1012 1016 1025 -13.352101
## 65 1001 1009 1013 1017 1025 -13.319949
## 66 1001 1010 1013 1019 1022 -13.272466
## 67 1003 1009 1015 1016 1022 -13.215507
## 68 1001 1008 1015 1019 1022 -13.159300
## 69 1001 1010 1012 1019 1023 -13.107187
## 70 1001 1008 1012 1019 1025 -13.005214
## 71 1002 1009 1015 1016 1023 -12.961267
## 72 1001 1009 1015 1017 1023 -12.885495
## 73 1005 1007 1014 1018 1021 -12.153624
## 74 1001 1007 1014 1018 1025 -11.795575
## 75 1005 1008 1014 1017 1021 -11.706232
## 76 1005 1006 1014 1018 1022 -11.619793
## 77 1001 1010 1014 1018 1022 -11.565541
## 78 1001 1008 1014 1020 1022 -11.465130
## 79 1005 1008 1014 1016 1022 -11.385869
## 80 1005 1006 1014 1017 1023 -11.379378
## 81 1003 1007 1014 1020 1021 -11.320430
## 82 1002 1008 1014 1020 1021 -11.315958
## 83 1002 1010 1014 1018 1021 -11.219287
## 84 1001 1007 1014 1020 1023 -11.122267
## 85 1005 1007 1014 1016 1023 -11.068054
## 86 1002 1006 1014 1020 1023 -11.003506
## 87 1003 1007 1014 1016 1025 -10.918061
## 88 1002 1006 1014 1018 1025 -10.848804
## 89 1003 1010 1014 1017 1021 -10.810011
## 90 1002 1008 1014 1016 1025 -10.805654
## 91 1001 1008 1014 1017 1025 -10.789959
## 92 1003 1006 1014 1020 1022 -10.751925
## 93 1003 1010 1014 1016 1022 -10.727691
## 94 1001 1010 1014 1017 1023 -10.545335
## 95 1002 1010 1014 1016 1023 -10.312417
## 96 1003 1006 1014 1017 1025 -10.003651
## 97 1004 1010 1011 1017 1023 -9.112803
## 98 1004 1007 1011 1020 1023 -8.998167
## 99 1004 1006 1015 1017 1023 -8.850351
## 100 1004 1007 1011 1018 1025 -8.812782
## 101 1004 1010 1012 1018 1021 -8.746495
## 102 1004 1006 1012 1020 1023 -8.650706
## 103 1004 1007 1015 1018 1021 -8.601730
## 104 1004 1010 1011 1018 1022 -8.528238
## 105 1004 1008 1015 1017 1021 -7.995112
## 106 1004 1010 1013 1017 1021 -7.907758
## 107 1004 1008 1012 1020 1021 -7.867624
## 108 1004 1008 1011 1017 1025 -7.860696
## 109 1004 1006 1012 1018 1025 -7.836200
## 110 1004 1006 1015 1018 1022 -7.822736
## 111 1004 1008 1011 1020 1022 -7.787201
## 112 1004 1006 1013 1017 1025 -7.667775
## 113 1004 1007 1013 1020 1021 -7.617443
## 114 1004 1006 1013 1020 1022 -7.447276
## 115 1004 1010 1012 1016 1023 -7.216149
## 116 1004 1007 1015 1016 1023 -7.099472
## 117 1004 1007 1013 1016 1025 -6.562529
## 118 1004 1008 1012 1016 1025 -6.476283
## 119 1004 1010 1013 1016 1022 -6.335508
## 120 1004 1008 1015 1016 1022 -6.254448
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -6.9 0.003 *** strongΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1005 1007 1011 1018 1024 -12.054810
## 2 1003 1007 1011 1020 1024 -11.803154
## 3 1005 1009 1011 1017 1023 -11.126213
## 4 1005 1008 1011 1017 1024 -11.071078
## 5 1003 1009 1011 1020 1022 -10.802225
## 6 1002 1010 1011 1018 1024 -10.757499
## 7 1003 1009 1011 1017 1025 -10.751161
## 8 1002 1009 1011 1018 1025 -10.736151
## 9 1002 1008 1011 1020 1024 -10.667773
## 10 1005 1009 1011 1018 1022 -10.657811
## 11 1003 1010 1011 1017 1024 -10.609852
## 12 1002 1009 1011 1020 1023 -10.604512
## 13 1002 1006 1013 1020 1024 -10.035626
## 14 1005 1007 1011 1019 1023 -10.018236
## 15 1005 1006 1013 1017 1024 -9.899918
## 16 1002 1006 1015 1019 1023 -9.587994
## 17 1005 1009 1013 1017 1021 -9.471900
## 18 1002 1010 1011 1019 1023 -9.406321
## 19 1002 1009 1013 1020 1021 -9.371688
## 20 1003 1007 1011 1019 1025 -9.345132
## 21 1002 1006 1015 1018 1024 -9.215810
## 22 1005 1007 1013 1016 1024 -8.972046
## 23 1003 1009 1012 1020 1021 -8.905591
## 24 1003 1009 1015 1017 1021 -8.903861
## 25 1005 1009 1012 1018 1021 -8.894043
## 26 1002 1008 1011 1019 1025 -8.877274
## 27 1003 1006 1015 1017 1024 -8.801382
## 28 1002 1009 1015 1018 1021 -8.766463
## 29 1005 1008 1011 1019 1022 -8.753358
## 30 1002 1008 1015 1019 1021 -8.734603
## 31 1005 1006 1012 1018 1024 -8.730925
## 32 1003 1007 1015 1019 1021 -8.707752
## 33 1002 1006 1013 1019 1025 -8.640731
## 34 1003 1010 1011 1019 1022 -8.632574
## 35 1003 1006 1012 1020 1024 -8.609615
## 36 1005 1007 1013 1019 1021 -8.579015
## 37 1002 1009 1013 1016 1025 -8.522420
## 38 1005 1006 1012 1019 1023 -8.471960
## 39 1005 1009 1013 1016 1022 -8.446023
## 40 1002 1010 1013 1019 1021 -8.377684
## 41 1005 1008 1012 1019 1021 -8.318841
## 42 1001 1007 1013 1020 1024 -8.306686
## 43 1001 1009 1013 1020 1022 -8.167377
## 44 1002 1010 1013 1016 1024 -8.129777
## 45 1005 1009 1012 1016 1023 -7.914338
## 46 1001 1009 1013 1017 1025 -7.890079
## 47 1003 1010 1012 1019 1021 -7.790210
## 48 1003 1006 1015 1019 1022 -7.765642
## 49 1005 1006 1013 1019 1022 -7.763462
## 50 1003 1009 1012 1016 1025 -7.565731
## 51 1001 1009 1012 1020 1023 -7.345760
## 52 1001 1010 1013 1017 1024 -7.326482
## 53 1002 1009 1015 1016 1023 -7.242529
## 54 1005 1008 1012 1016 1024 -7.210439
## 55 1003 1007 1015 1016 1024 -7.109512
## 56 1004 1007 1011 1020 1023 -7.055347
## 57 1001 1009 1012 1018 1025 -7.054112
## 58 1003 1009 1015 1016 1022 -7.044866
## 59 1003 1006 1012 1019 1025 -6.958326
## 60 1001 1009 1015 1017 1023 -6.893848
## 61 1002 1008 1015 1016 1024 -6.857085
## 62 1004 1007 1011 1018 1025 -6.714248
## 63 1003 1010 1012 1016 1024 -6.708811
## 64 1001 1008 1012 1020 1024 -6.654756
## 65 1001 1009 1015 1018 1022 -6.630876
## 66 1004 1010 1011 1017 1023 -6.616151
## 67 1001 1007 1015 1018 1024 -6.498557
## 68 1001 1007 1013 1019 1025 -6.497803
## 69 1004 1006 1015 1017 1023 -6.330674
## 70 1001 1008 1015 1017 1024 -6.206119
## 71 1001 1010 1012 1018 1024 -6.064642
## 72 1001 1010 1013 1019 1022 -5.991661
## 73 1004 1007 1015 1018 1021 -5.869095
## 74 1001 1007 1015 1019 1023 -5.821836
## 75 1004 1010 1011 1018 1022 -5.807997
## 76 1004 1006 1012 1020 1023 -5.719828
## 77 1004 1008 1011 1017 1025 -5.564127
## 78 1004 1008 1011 1020 1022 -5.354068
## 79 1004 1008 1015 1017 1021 -5.291104
## 80 1004 1010 1012 1018 1021 -5.275769
## 81 1001 1010 1012 1019 1023 -5.271513
## 82 1001 1008 1015 1019 1022 -5.220998
## 83 1001 1008 1012 1019 1025 -5.138572
## 84 1004 1006 1013 1017 1025 -5.036109
## 85 1004 1007 1013 1020 1021 -4.924594
## 86 1004 1006 1015 1018 1022 -4.896623
## 87 1004 1010 1013 1017 1021 -4.875328
## 88 1004 1008 1012 1020 1021 -4.669094
## 89 1004 1006 1013 1020 1022 -4.643646
## 90 1004 1006 1012 1018 1025 -4.583162
## 91 1004 1007 1015 1016 1023 -4.138863
## 92 1004 1007 1013 1016 1025 -4.084905
## 93 1004 1010 1012 1016 1023 -3.876373
## 94 1004 1010 1013 1016 1022 -3.502969
## 95 1002 1006 1014 1020 1023 -3.003262
## 96 1004 1008 1012 1016 1025 -2.995248
## 97 1002 1006 1014 1018 1025 -2.929535
## 98 1004 1008 1015 1016 1022 -2.804403
## 99 1003 1007 1014 1020 1021 -2.658629
## 100 1005 1007 1014 1018 1021 -2.550593
## 101 1002 1010 1014 1018 1021 -2.521081
## 102 1002 1008 1014 1020 1021 -2.413307
## 103 1005 1006 1014 1017 1023 -2.379781
## 104 1003 1006 1014 1017 1025 -2.292904
## 105 1003 1010 1014 1017 1021 -2.266466
## 106 1003 1006 1014 1020 1022 -2.227059
## 107 1005 1008 1014 1017 1021 -2.205381
## 108 1003 1007 1014 1016 1025 -2.180527
## 109 1001 1007 1014 1018 1025 -2.018480
## 110 1002 1008 1014 1016 1025 -1.998963
## 111 1005 1007 1014 1016 1023 -1.946245
## 112 1005 1006 1014 1018 1022 -1.888324
## 113 1002 1010 1014 1016 1023 -1.852978
## 114 1003 1010 1014 1016 1022 -1.847996
## 115 1001 1007 1014 1020 1023 -1.823960
## 116 1001 1008 1014 1020 1022 -1.789733
## 117 1001 1010 1014 1018 1022 -1.701390
## 118 1005 1008 1014 1016 1022 -1.613748
## 119 1001 1008 1014 1017 1025 -1.576207
## 120 1001 1010 1014 1017 1023 -1.406701MM
metaecosystem_type_selected = c("Medium-Medium")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.7 0.188 noneΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1047 1052 -7.0607335
## 2 1052 1047 -7.0607335
## 3 1050 1055 -6.8797275
## 4 1055 1050 -6.8797275
## 5 1052 1053 -5.7371488
## 6 1053 1052 -5.7371488
## 7 1047 1055 -4.9047537
## 8 1055 1047 -4.9047537
## 9 1047 1051 -3.1078158
## 10 1051 1047 -3.1078158
## 11 1046 1055 -1.1276198
## 12 1055 1046 -1.1276198
## 13 1051 1054 -0.7159126
## 14 1054 1051 -0.7159126
## 15 1049 1053 0.6570313
## 16 1053 1049 0.6570313
## 17 1046 1053 0.8298717
## 18 1053 1046 0.8298717
## 19 1048 1050 1.0319298
## 20 1050 1048 1.0319298
## 21 1048 1052 1.3554353
## 22 1052 1048 1.3554353
## 23 1049 1050 1.6240907
## 24 1050 1049 1.6240907
## 25 1046 1054 1.8310059
## 26 1054 1046 1.8310059
## 27 1049 1051 1.8319359
## 28 1051 1049 1.8319359
## 29 1048 1054 3.1286549
## 30 1054 1048 3.1286549
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.7 0.098 * weakΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1047 1052 -9.0420799
## 2 1052 1047 -9.0420799
## 3 1052 1053 -7.6293919
## 4 1053 1052 -7.6293919
## 5 1047 1055 -5.6355950
## 6 1055 1047 -5.6355950
## 7 1047 1051 -3.9563482
## 8 1051 1047 -3.9563482
## 9 1049 1053 -1.2713678
## 10 1053 1049 -1.2713678
## 11 1050 1055 -1.0400315
## 12 1055 1050 -1.0400315
## 13 1051 1054 -0.8225792
## 14 1054 1051 -0.8225792
## 15 1046 1053 -0.7316877
## 16 1053 1046 -0.7316877
## 17 1048 1052 -0.2472453
## 18 1052 1048 -0.2472453
## 19 1046 1055 0.0678831
## 20 1055 1046 0.0678831
## 21 1049 1051 0.2381335
## 22 1051 1049 0.2381335
## 23 1046 1054 0.8015445
## 24 1054 1046 0.8015445
## 25 1049 1050 0.9316284
## 26 1050 1049 0.9316284
## 27 1048 1054 1.6906341
## 28 1054 1048 1.6906341
## 29 1048 1050 1.8004495
## 30 1050 1048 1.8004495Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: SL (connected vs unconnected) and MM (connected vs unconnected).
Gamma
response_variable_selected = "metaecosystem_richness"metaecosystem_type_selected = c("Medium-Medium",
"Small-Large")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
SL
metaecosystem_type_selected = c("Small-Large")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: optimx (L-BFGS-B)"
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: optimx (L-BFGS-B)"
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: nlminbwrap "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: nlminbwrap "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: optimx (L-BFGS-B)"
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: optimx (L-BFGS-B)"
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1 0.228 noneΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1005 1006 1012 1018 1024 -1.778904826
## 2 1003 1006 1012 1020 1024 -1.718037130
## 3 1004 1006 1012 1018 1025 -1.547129228
## 4 1003 1006 1015 1017 1024 -1.385572293
## 5 1003 1006 1012 1019 1025 -1.264075050
## 6 1005 1006 1013 1017 1024 -1.166808812
## 7 1004 1006 1013 1017 1025 -1.008561113
## 8 1004 1006 1015 1018 1022 -0.944926703
## 9 1004 1010 1012 1018 1021 -0.875111995
## 10 1003 1010 1012 1016 1024 -0.678955036
## 11 1004 1006 1013 1020 1022 -0.618020661
## 12 1004 1008 1015 1017 1021 -0.420708033
## 13 1004 1008 1012 1020 1021 -0.414392196
## 14 1004 1008 1012 1016 1025 -0.373534029
## 15 1005 1006 1012 1019 1023 -0.355240112
## 16 1004 1010 1013 1017 1021 -0.325994676
## 17 1004 1006 1015 1017 1023 -0.315069376
## 18 1004 1006 1012 1020 1023 -0.285816573
## 19 1003 1006 1015 1019 1022 -0.241043607
## 20 1003 1010 1012 1019 1021 -0.200868914
## 21 1004 1007 1015 1018 1021 -0.138404548
## 22 1004 1010 1013 1016 1022 -0.110972007
## 23 1004 1010 1011 1018 1022 -0.054404591
## 24 1004 1008 1015 1016 1022 -0.010609720
## 25 1005 1008 1012 1016 1024 -0.001907889
## 26 1003 1006 1014 1017 1025 0.007503791
## 27 1005 1008 1012 1019 1021 0.009311033
## 28 1003 1009 1012 1020 1021 0.026186592
## 29 1005 1006 1013 1019 1022 0.051672424
## 30 1003 1009 1012 1016 1025 0.053479059
## 31 1005 1009 1012 1018 1021 0.175087994
## 32 1004 1007 1013 1020 1021 0.219802387
## 33 1004 1010 1012 1016 1023 0.276154705
## 34 1005 1006 1014 1017 1023 0.333974941
## 35 1004 1007 1013 1016 1025 0.346289331
## 36 1003 1007 1015 1016 1024 0.358493848
## 37 1003 1009 1015 1017 1021 0.376021815
## 38 1005 1006 1014 1018 1022 0.409040896
## 39 1001 1010 1012 1018 1024 0.423327947
## 40 1003 1007 1015 1019 1021 0.457421385
## 41 1004 1008 1011 1017 1025 0.472731611
## 42 1004 1008 1011 1020 1022 0.514714685
## 43 1005 1009 1013 1017 1021 0.576437111
## 44 1003 1010 1011 1019 1022 0.656637935
## 45 1005 1007 1013 1016 1024 0.665315948
## 46 1004 1007 1011 1018 1025 0.674381115
## 47 1003 1010 1011 1017 1024 0.680584118
## 48 1004 1010 1011 1017 1023 0.781676151
## 49 1004 1007 1015 1016 1023 0.786123228
## 50 1005 1007 1013 1019 1021 0.790934777
## 51 1002 1006 1015 1018 1024 0.791434390
## 52 1005 1008 1014 1017 1021 0.794546798
## 53 1003 1006 1014 1020 1022 0.817179695
## 54 1003 1009 1015 1016 1022 0.856215044
## 55 1001 1008 1012 1019 1025 0.898480697
## 56 1001 1010 1013 1017 1024 0.906499597
## 57 1001 1008 1012 1020 1024 0.945901021
## 58 1002 1006 1013 1020 1024 0.993600522
## 59 1001 1009 1012 1018 1025 1.031619470
## 60 1003 1010 1014 1017 1021 1.038201638
## 61 1003 1010 1014 1016 1022 1.051692128
## 62 1001 1008 1015 1017 1024 1.083552457
## 63 1005 1009 1012 1016 1023 1.096239919
## 64 1005 1009 1013 1016 1022 1.101736624
## 65 1005 1008 1014 1016 1022 1.119014927
## 66 1005 1007 1014 1018 1021 1.125138628
## 67 1003 1007 1011 1020 1024 1.148110566
## 68 1001 1007 1015 1018 1024 1.169035787
## 69 1003 1007 1011 1019 1025 1.177307467
## 70 1003 1007 1014 1016 1025 1.194118362
## 71 1005 1008 1011 1019 1022 1.205594748
## 72 1005 1008 1011 1017 1024 1.292515127
## 73 1001 1010 1012 1019 1023 1.307913875
## 74 1005 1007 1011 1018 1024 1.344736150
## 75 1004 1007 1011 1020 1023 1.360531062
## 76 1005 1007 1014 1016 1023 1.363102937
## 77 1001 1009 1013 1017 1025 1.394059215
## 78 1001 1008 1015 1019 1022 1.434802806
## 79 1001 1007 1013 1020 1024 1.435316966
## 80 1003 1007 1014 1020 1021 1.446790143
## 81 1001 1010 1013 1019 1022 1.447593214
## 82 1001 1008 1014 1017 1025 1.465884494
## 83 1003 1009 1011 1017 1025 1.480973254
## 84 1003 1009 1011 1020 1022 1.493649122
## 85 1002 1009 1013 1020 1021 1.543726361
## 86 1001 1007 1013 1019 1025 1.597028665
## 87 1001 1009 1015 1018 1022 1.618149711
## 88 1002 1009 1015 1018 1021 1.618169224
## 89 1002 1006 1013 1019 1025 1.651233214
## 90 1001 1009 1013 1020 1022 1.652180899
## 91 1005 1009 1011 1018 1022 1.701735381
## 92 1001 1010 1014 1018 1022 1.717711732
## 93 1005 1007 1011 1019 1023 1.739874892
## 94 1001 1007 1014 1018 1025 1.784354975
## 95 1001 1010 1014 1017 1023 1.803646532
## 96 1001 1009 1012 1020 1023 1.805835673
## 97 1001 1007 1015 1019 1023 1.871420898
## 98 1002 1008 1015 1019 1021 1.946531960
## 99 1002 1010 1013 1016 1024 1.959416156
## 100 1002 1009 1013 1016 1025 1.964498415
## 101 1002 1006 1015 1019 1023 1.977253733
## 102 1002 1010 1011 1018 1024 1.978097053
## 103 1002 1008 1015 1016 1024 1.979208725
## 104 1001 1009 1015 1017 1023 2.021416410
## 105 1002 1008 1011 1020 1024 2.094187494
## 106 1001 1008 1014 1020 1022 2.131235905
## 107 1005 1009 1011 1017 1023 2.143312099
## 108 1002 1006 1014 1018 1025 2.144558419
## 109 1002 1009 1011 1018 1025 2.249400597
## 110 1002 1010 1013 1019 1021 2.369644955
## 111 1002 1008 1011 1019 1025 2.420073136
## 112 1001 1007 1014 1020 1023 2.436615704
## 113 1002 1009 1015 1016 1023 2.514484269
## 114 1002 1010 1011 1019 1023 2.613271192
## 115 1002 1009 1011 1020 1023 2.702690385
## 116 1002 1006 1014 1020 1023 2.786732349
## 117 1002 1010 1014 1018 1021 2.911085556
## 118 1002 1008 1014 1020 1021 2.961682219
## 119 1002 1008 1014 1016 1025 3.003137511
## 120 1002 1010 1014 1016 1023 3.214292666
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.2 0.175 noneΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1003 1006 1012 1019 1025 -2.219358013
## 2 1005 1006 1012 1018 1024 -2.059679682
## 3 1005 1006 1012 1019 1023 -1.931806483
## 4 1003 1006 1014 1017 1025 -1.711301720
## 5 1005 1006 1014 1017 1023 -1.650302367
## 6 1005 1006 1013 1017 1024 -1.625578728
## 7 1003 1006 1012 1020 1024 -1.470048283
## 8 1003 1006 1015 1017 1024 -1.415450130
## 9 1005 1006 1014 1018 1022 -1.385085638
## 10 1004 1006 1012 1018 1025 -1.215692566
## 11 1005 1008 1012 1019 1021 -1.191223658
## 12 1005 1006 1013 1019 1022 -1.124034660
## 13 1003 1006 1015 1019 1022 -1.048186281
## 14 1005 1008 1014 1017 1021 -1.016368639
## 15 1003 1010 1012 1016 1024 -0.914151725
## 16 1003 1010 1012 1019 1021 -0.897779891
## 17 1005 1008 1012 1016 1024 -0.813977398
## 18 1005 1008 1014 1016 1022 -0.777597672
## 19 1004 1008 1012 1016 1025 -0.728713791
## 20 1004 1006 1013 1017 1025 -0.715238216
## 21 1003 1006 1014 1020 1022 -0.691714909
## 22 1005 1007 1014 1016 1023 -0.631052544
## 23 1001 1008 1012 1019 1025 -0.587337277
## 24 1005 1007 1014 1018 1021 -0.568638572
## 25 1003 1007 1014 1016 1025 -0.566310438
## 26 1003 1010 1014 1016 1022 -0.564102937
## 27 1004 1006 1015 1017 1023 -0.514753479
## 28 1004 1006 1015 1018 1022 -0.507781873
## 29 1001 1008 1014 1017 1025 -0.494455013
## 30 1003 1010 1014 1017 1021 -0.462026430
## 31 1004 1010 1012 1018 1021 -0.388732541
## 32 1005 1007 1013 1019 1021 -0.366504729
## 33 1004 1006 1012 1020 1023 -0.365342151
## 34 1001 1010 1012 1019 1023 -0.332059098
## 35 1004 1008 1015 1017 1021 -0.307642334
## 36 1004 1010 1012 1016 1023 -0.301104238
## 37 1004 1008 1015 1016 1022 -0.201308571
## 38 1003 1007 1015 1019 1021 -0.196896829
## 39 1001 1010 1014 1017 1023 -0.186114872
## 40 1005 1007 1013 1016 1024 -0.140268470
## 41 1004 1008 1012 1020 1021 -0.120352082
## 42 1001 1010 1012 1018 1024 -0.106250688
## 43 1001 1007 1014 1018 1025 -0.103675499
## 44 1004 1007 1013 1016 1025 -0.078385824
## 45 1001 1010 1014 1018 1022 -0.073719216
## 46 1004 1006 1013 1020 1022 -0.067276983
## 47 1004 1010 1013 1016 1022 -0.050607175
## 48 1004 1007 1015 1018 1021 -0.007607146
## 49 1003 1009 1012 1016 1025 -0.002085895
## 50 1005 1008 1011 1019 1022 0.011887907
## 51 1003 1007 1015 1016 1024 0.014014020
## 52 1003 1010 1011 1019 1022 0.024106329
## 53 1004 1007 1015 1016 1023 0.032018034
## 54 1004 1010 1011 1018 1022 0.052408292
## 55 1004 1010 1013 1017 1021 0.052926251
## 56 1001 1008 1015 1019 1022 0.112776231
## 57 1004 1010 1011 1017 1023 0.128178924
## 58 1005 1007 1011 1019 1023 0.133580369
## 59 1001 1007 1013 1019 1025 0.148012106
## 60 1003 1007 1014 1020 1021 0.150475834
## 61 1005 1009 1012 1016 1023 0.176976521
## 62 1004 1008 1011 1017 1025 0.192771965
## 63 1001 1010 1013 1019 1022 0.208347751
## 64 1001 1010 1013 1017 1024 0.232317142
## 65 1001 1007 1015 1019 1023 0.258989920
## 66 1001 1008 1015 1017 1024 0.273175471
## 67 1003 1007 1011 1019 1025 0.298142709
## 68 1005 1009 1012 1018 1021 0.346079707
## 69 1001 1008 1014 1020 1022 0.346902565
## 70 1002 1006 1014 1018 1025 0.364794589
## 71 1001 1008 1012 1020 1024 0.387886785
## 72 1004 1007 1011 1018 1025 0.392393888
## 73 1004 1007 1013 1020 1021 0.405988440
## 74 1001 1007 1015 1018 1024 0.482890066
## 75 1005 1008 1011 1017 1024 0.486647132
## 76 1002 1006 1013 1019 1025 0.495154043
## 77 1002 1006 1015 1018 1024 0.496310995
## 78 1001 1007 1014 1020 1023 0.500554237
## 79 1003 1010 1011 1017 1024 0.519961102
## 80 1002 1006 1015 1019 1023 0.520191712
## 81 1004 1008 1011 1020 1022 0.539178720
## 82 1005 1009 1013 1017 1021 0.658859305
## 83 1005 1007 1011 1018 1024 0.662592247
## 84 1004 1007 1011 1020 1023 0.702502271
## 85 1003 1009 1012 1020 1021 0.717433884
## 86 1001 1009 1012 1018 1025 0.725538800
## 87 1003 1009 1015 1017 1021 0.740027648
## 88 1005 1009 1013 1016 1022 0.749330936
## 89 1003 1009 1015 1016 1022 0.754624454
## 90 1002 1006 1013 1020 1024 0.804710870
## 91 1001 1007 1013 1020 1024 0.839928174
## 92 1005 1009 1011 1017 1023 0.897932466
## 93 1002 1006 1014 1020 1023 0.899347495
## 94 1001 1009 1013 1017 1025 1.012013654
## 95 1005 1009 1011 1018 1022 1.034052768
## 96 1002 1008 1015 1019 1021 1.063714785
## 97 1001 1009 1015 1017 1023 1.065738034
## 98 1002 1008 1014 1016 1025 1.080267417
## 99 1003 1009 1011 1017 1025 1.084833829
## 100 1003 1007 1011 1020 1024 1.093580225
## 101 1001 1009 1012 1020 1023 1.097526419
## 102 1001 1009 1015 1018 1022 1.180888874
## 103 1002 1010 1013 1016 1024 1.223397671
## 104 1002 1010 1014 1016 1023 1.241595386
## 105 1002 1008 1015 1016 1024 1.265946669
## 106 1002 1010 1011 1019 1023 1.278263577
## 107 1002 1010 1014 1018 1021 1.334858820
## 108 1003 1009 1011 1020 1022 1.345350972
## 109 1002 1010 1013 1019 1021 1.370037816
## 110 1001 1009 1013 1020 1022 1.447562357
## 111 1002 1008 1011 1019 1025 1.452959945
## 112 1002 1008 1014 1020 1021 1.473883808
## 113 1002 1009 1015 1016 1023 1.543179254
## 114 1002 1009 1013 1016 1025 1.611291586
## 115 1002 1010 1011 1018 1024 1.677338893
## 116 1002 1009 1015 1018 1021 1.687888414
## 117 1002 1009 1011 1018 1025 1.827296802
## 118 1002 1009 1013 1020 1021 1.849794733
## 119 1002 1009 1011 1020 1023 1.855236500
## 120 1002 1008 1011 1020 1024 1.885207997MM
metaecosystem_type_selected = c("Medium-Medium")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.336 noneΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1048 1052 -1.475403182
## 2 1052 1048 -1.475403182
## 3 1052 1053 0.003672664
## 4 1053 1052 0.003672664
## 5 1048 1050 0.058504809
## 6 1050 1048 0.058504809
## 7 1047 1052 0.433427147
## 8 1052 1047 0.433427147
## 9 1046 1053 0.867464578
## 10 1053 1046 0.867464578
## 11 1047 1051 1.209882576
## 12 1051 1047 1.209882576
## 13 1050 1055 1.393616601
## 14 1055 1050 1.393616601
## 15 1046 1055 1.817874264
## 16 1055 1046 1.817874264
## 17 1046 1054 1.826880301
## 18 1054 1046 1.826880301
## 19 1048 1054 1.986688934
## 20 1054 1048 1.986688934
## 21 1047 1055 1.994237408
## 22 1055 1047 1.994237408
## 23 1051 1054 2.144335580
## 24 1054 1051 2.144335580
## 25 1049 1051 2.487241386
## 26 1051 1049 2.487241386
## 27 1049 1053 2.495267601
## 28 1053 1049 2.495267601
## 29 1049 1050 2.556965452
## 30 1050 1049 2.556965452
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.2 0.178 noneΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1052 1053 -1.8955591
## 2 1053 1052 -1.8955591
## 3 1046 1053 -0.6712230
## 4 1053 1046 -0.6712230
## 5 1050 1055 -0.6037116
## 6 1055 1050 -0.6037116
## 7 1047 1051 -0.5579459
## 8 1051 1047 -0.5579459
## 9 1048 1050 -0.3193849
## 10 1050 1048 -0.3193849
## 11 1048 1052 0.1233223
## 12 1052 1048 0.1233223
## 13 1047 1052 0.1234953
## 14 1052 1047 0.1234953
## 15 1047 1055 0.1834023
## 16 1055 1047 0.1834023
## 17 1051 1054 0.2683769
## 18 1054 1051 0.2683769
## 19 1048 1054 0.3686785
## 20 1054 1048 0.3686785
## 21 1046 1055 0.4611048
## 22 1055 1046 0.4611048
## 23 1049 1053 0.6697885
## 24 1053 1049 0.6697885
## 25 1049 1051 0.9131296
## 26 1051 1049 0.9131296
## 27 1049 1050 1.4509424
## 28 1050 1049 1.4509424
## 29 1046 1054 1.5654721
## 30 1054 1046 1.5654721Biomass
response_variable_selected = "total_metaecosystem_bioarea_mm2"metaecosystem_type_selected = c("Medium-Medium",
"Small-Large")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: SL (connected vs unconnected) and MM (connected vs unconnected).
SL
metaecosystem_type_selected = c("Small-Large")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
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## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
## [1] "Model successfully fitted with optimizer: bobyqa "
Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.2 0.149 noneΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1001 1009 1012 1018 1025 -0.2683468225
## 2 1001 1008 1012 1019 1025 -0.2454554939
## 3 1003 1009 1012 1016 1025 -0.2084818604
## 4 1003 1006 1012 1019 1025 -0.1638806050
## 5 1001 1008 1012 1020 1024 -0.1099938438
## 6 1003 1009 1011 1017 1025 -0.0987884114
## 7 1003 1009 1012 1020 1021 -0.0721910535
## 8 1001 1008 1014 1017 1025 -0.0553092234
## 9 1001 1008 1015 1019 1022 -0.0512412726
## 10 1001 1009 1012 1020 1023 -0.0499965654
## 11 1001 1009 1015 1018 1022 -0.0299693819
## 12 1003 1009 1015 1017 1021 -0.0279557551
## 13 1003 1007 1011 1019 1025 -0.0173031011
## 14 1003 1006 1015 1019 1022 -0.0170268418
## 15 1003 1009 1015 1016 1022 -0.0056082635
## 16 1005 1008 1012 1019 1021 -0.0048332039
## 17 1002 1009 1011 1018 1025 -0.0004212474
## 18 1005 1009 1012 1018 1021 0.0018432505
## 19 1002 1008 1015 1019 1021 0.0030855825
## 20 1002 1008 1011 1019 1025 0.0041406399
## 21 1003 1007 1015 1019 1021 0.0108962162
## 22 1005 1008 1012 1016 1024 0.0177898111
## 23 1001 1008 1015 1017 1024 0.0214037646
## 24 1002 1009 1015 1018 1021 0.0337086996
## 25 1003 1006 1014 1017 1025 0.0346624703
## 26 1003 1009 1011 1020 1022 0.0381533916
## 27 1001 1010 1012 1018 1024 0.0506890914
## 28 1003 1006 1012 1020 1024 0.0517535213
## 29 1003 1010 1012 1019 1021 0.0525448504
## 30 1002 1008 1014 1016 1025 0.0586825316
## 31 1001 1007 1014 1018 1025 0.0657920723
## 32 1001 1009 1015 1017 1023 0.0730983414
## 33 1005 1009 1012 1016 1023 0.0820554287
## 34 1001 1008 1014 1020 1022 0.0860331083
## 35 1003 1010 1012 1016 1024 0.0929643618
## 36 1003 1007 1014 1016 1025 0.0932894741
## 37 1003 1006 1015 1017 1024 0.0968529116
## 38 1005 1008 1011 1017 1024 0.0971863756
## 39 1005 1008 1011 1019 1022 0.0991505125
## 40 1005 1009 1011 1018 1022 0.1125744073
## 41 1001 1010 1012 1019 1023 0.1140497254
## 42 1005 1006 1012 1018 1024 0.1148109878
## 43 1001 1007 1015 1018 1024 0.1213672481
## 44 1002 1006 1014 1018 1025 0.1239664036
## 45 1003 1010 1011 1019 1022 0.1302450955
## 46 1002 1008 1015 1016 1024 0.1325186375
## 47 1001 1007 1015 1019 1023 0.1416835828
## 48 1002 1008 1011 1020 1024 0.1438621768
## 49 1005 1008 1014 1017 1021 0.1459421379
## 50 1003 1007 1015 1016 1024 0.1486564756
## 51 1003 1010 1011 1017 1024 0.1487282051
## 52 1005 1006 1012 1019 1023 0.1542102863
## 53 1005 1008 1014 1016 1022 0.1581073437
## 54 1005 1009 1011 1017 1023 0.1690615383
## 55 1003 1006 1014 1020 1022 0.1694577248
## 56 1003 1007 1011 1020 1024 0.1717822595
## 57 1002 1006 1015 1018 1024 0.1745939468
## 58 1002 1008 1014 1020 1021 0.1749037263
## 59 1002 1006 1015 1019 1023 0.1808814100
## 60 1002 1009 1015 1016 1023 0.1844881895
## 61 1004 1008 1012 1016 1025 0.1948745221
## 62 1002 1009 1011 1020 1023 0.2086995377
## 63 1003 1007 1014 1020 1021 0.2145802194
## 64 1001 1010 1014 1018 1022 0.2162895407
## 65 1003 1010 1014 1017 1021 0.2223999197
## 66 1004 1006 1012 1018 1025 0.2248748144
## 67 1004 1008 1015 1017 1021 0.2286229572
## 68 1003 1010 1014 1016 1022 0.2309148725
## 69 1005 1006 1014 1018 1022 0.2349267578
## 70 1004 1008 1015 1016 1022 0.2419978151
## 71 1005 1007 1011 1018 1024 0.2425460381
## 72 1004 1006 1015 1018 1022 0.2463745510
## 73 1002 1010 1011 1018 1024 0.2563204004
## 74 1005 1007 1014 1018 1021 0.2847099526
## 75 1005 1007 1011 1019 1023 0.2866743792
## 76 1004 1008 1011 1017 1025 0.2879210975
## 77 1004 1007 1015 1018 1021 0.2913289426
## 78 1004 1008 1012 1020 1021 0.2979974140
## 79 1002 1010 1014 1018 1021 0.3049729590
## 80 1002 1010 1011 1019 1023 0.3103581812
## 81 1001 1010 1014 1017 1023 0.3522940304
## 82 1004 1007 1011 1018 1025 0.3553969485
## 83 1001 1009 1013 1017 1025 0.3579632057
## 84 1001 1007 1014 1020 1023 0.3618545769
## 85 1005 1006 1014 1017 1023 0.3758791146
## 86 1004 1008 1011 1020 1022 0.3841110898
## 87 1004 1010 1012 1018 1021 0.3889350822
## 88 1004 1006 1015 1017 1023 0.4060196860
## 89 1002 1006 1014 1020 1023 0.4197892202
## 90 1005 1007 1014 1016 1023 0.4426687234
## 91 1004 1010 1011 1018 1022 0.4453434887
## 92 1001 1009 1013 1020 1022 0.4463930560
## 93 1004 1006 1012 1020 1023 0.4616285894
## 94 1002 1010 1014 1016 1023 0.4668071699
## 95 1004 1007 1015 1016 1023 0.4707332751
## 96 1001 1007 1013 1019 1025 0.4738501769
## 97 1001 1010 1013 1017 1024 0.4818174381
## 98 1004 1010 1012 1016 1023 0.4962512608
## 99 1001 1010 1013 1019 1022 0.5061870346
## 100 1002 1009 1013 1016 1025 0.5198811871
## 101 1005 1009 1013 1016 1022 0.5283602683
## 102 1005 1009 1013 1017 1021 0.5295623824
## 103 1004 1010 1011 1017 1023 0.5480751233
## 104 1001 1007 1013 1020 1024 0.5582233921
## 105 1002 1006 1013 1019 1025 0.5734486267
## 106 1004 1007 1011 1020 1023 0.5828436353
## 107 1005 1006 1013 1017 1024 0.5847651773
## 108 1005 1006 1013 1019 1022 0.5850660366
## 109 1002 1009 1013 1020 1021 0.6010631809
## 110 1005 1007 1013 1016 1024 0.6301339432
## 111 1002 1010 1013 1016 1024 0.6372269987
## 112 1005 1007 1013 1019 1021 0.6387527780
## 113 1002 1010 1013 1019 1021 0.6395254010
## 114 1002 1006 1013 1020 1024 0.6879250699
## 115 1004 1006 1013 1017 1025 0.8439821326
## 116 1004 1010 1013 1016 1022 0.8688078132
## 117 1004 1010 1013 1017 1021 0.8755440867
## 118 1004 1006 1013 1020 1022 0.8887790216
## 119 1004 1007 1013 1016 1025 0.8956529471
## 120 1004 1007 1013 1020 1021 0.9456796479
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -1.6 0.057 * weakΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1001 1008 1012 1019 1025 -2.182491
## 2 1001 1009 1012 1018 1025 -2.172731
## 3 1003 1009 1012 1016 1025 -2.107717
## 4 1001 1008 1012 1020 1024 -2.102531
## 5 1001 1009 1012 1020 1023 -2.026749
## 6 1003 1006 1012 1019 1025 -2.015332
## 7 1003 1009 1011 1017 1025 -1.990367
## 8 1005 1008 1012 1016 1024 -1.971602
## 9 1003 1009 1012 1020 1021 -1.943598
## 10 1001 1010 1012 1018 1024 -1.938769
## 11 1001 1008 1015 1017 1024 -1.927036
## 12 1005 1008 1012 1019 1021 -1.907384
## 13 1003 1010 1012 1016 1024 -1.896069
## 14 1003 1006 1012 1020 1024 -1.894695
## 15 1002 1008 1011 1019 1025 -1.892851
## 16 1005 1008 1011 1017 1024 -1.891832
## 17 1005 1009 1012 1016 1023 -1.887131
## 18 1001 1008 1015 1019 1022 -1.884560
## 19 1001 1010 1012 1019 1023 -1.876738
## 20 1005 1009 1012 1018 1021 -1.864973
## 21 1003 1010 1012 1019 1021 -1.853563
## 22 1003 1007 1011 1019 1025 -1.853158
## 23 1002 1009 1011 1018 1025 -1.849551
## 24 1001 1009 1015 1017 1023 -1.841241
## 25 1003 1010 1011 1017 1024 -1.839583
## 26 1002 1008 1011 1020 1024 -1.838138
## 27 1005 1006 1012 1018 1024 -1.830593
## 28 1003 1009 1011 1020 1022 -1.822542
## 29 1001 1009 1015 1018 1022 -1.821596
## 30 1003 1009 1015 1017 1021 -1.802862
## 31 1001 1008 1014 1017 1025 -1.798684
## 32 1005 1009 1011 1017 1023 -1.793213
## 33 1002 1008 1015 1016 1024 -1.789985
## 34 1005 1006 1012 1019 1023 -1.788693
## 35 1005 1008 1011 1019 1022 -1.785180
## 36 1003 1009 1015 1016 1022 -1.784588
## 37 1003 1006 1015 1017 1024 -1.781299
## 38 1003 1007 1011 1020 1024 -1.775515
## 39 1002 1008 1015 1019 1021 -1.773676
## 40 1001 1007 1015 1018 1024 -1.772379
## 41 1003 1010 1011 1019 1022 -1.760197
## 42 1003 1006 1015 1019 1022 -1.750785
## 43 1004 1008 1012 1016 1025 -1.749543
## 44 1001 1007 1015 1019 1023 -1.748338
## 45 1002 1009 1011 1020 1023 -1.741951
## 46 1003 1007 1015 1016 1024 -1.737956
## 47 1005 1009 1011 1018 1022 -1.726848
## 48 1003 1007 1015 1019 1021 -1.725151
## 49 1002 1010 1011 1018 1024 -1.715813
## 50 1005 1007 1011 1018 1024 -1.694444
## 51 1002 1009 1015 1016 1023 -1.692816
## 52 1002 1009 1015 1018 1021 -1.692678
## 53 1002 1006 1015 1018 1024 -1.669624
## 54 1002 1010 1011 1019 1023 -1.660091
## 55 1002 1006 1015 1019 1023 -1.656766
## 56 1004 1008 1011 1017 1025 -1.649427
## 57 1004 1006 1012 1018 1025 -1.645578
## 58 1005 1007 1011 1019 1023 -1.643164
## 59 1004 1008 1012 1020 1021 -1.627684
## 60 1001 1008 1014 1020 1022 -1.619271
## 61 1004 1008 1015 1017 1021 -1.615768
## 62 1001 1009 1013 1017 1025 -1.605184
## 63 1002 1008 1014 1016 1025 -1.603539
## 64 1004 1008 1015 1016 1022 -1.599449
## 65 1003 1006 1014 1017 1025 -1.598682
## 66 1001 1007 1014 1018 1025 -1.588177
## 67 1005 1008 1014 1017 1021 -1.545813
## 68 1003 1007 1014 1016 1025 -1.532989
## 69 1004 1010 1012 1018 1021 -1.532754
## 70 1001 1010 1014 1017 1023 -1.527251
## 71 1004 1008 1011 1020 1022 -1.526116
## 72 1001 1010 1013 1017 1024 -1.516370
## 73 1005 1008 1014 1016 1022 -1.510757
## 74 1004 1006 1015 1018 1022 -1.509596
## 75 1001 1010 1014 1018 1022 -1.505000
## 76 1001 1009 1013 1020 1022 -1.500836
## 77 1004 1010 1012 1016 1023 -1.496412
## 78 1004 1006 1012 1020 1023 -1.495044
## 79 1003 1010 1014 1017 1021 -1.493156
## 80 1004 1007 1011 1018 1025 -1.485052
## 81 1004 1006 1015 1017 1023 -1.483121
## 82 1001 1007 1013 1019 1025 -1.469007
## 83 1004 1007 1015 1018 1021 -1.468101
## 84 1001 1010 1013 1019 1022 -1.467684
## 85 1003 1010 1014 1016 1022 -1.466879
## 86 1002 1008 1014 1020 1021 -1.457733
## 87 1004 1010 1011 1018 1022 -1.448915
## 88 1004 1010 1011 1017 1023 -1.440425
## 89 1002 1006 1014 1018 1025 -1.439584
## 90 1001 1007 1014 1020 1023 -1.438312
## 91 1001 1007 1013 1020 1024 -1.436174
## 92 1003 1006 1014 1020 1022 -1.424139
## 93 1004 1007 1015 1016 1023 -1.421432
## 94 1002 1009 1013 1016 1025 -1.416773
## 95 1005 1009 1013 1017 1021 -1.413995
## 96 1005 1009 1013 1016 1022 -1.412656
## 97 1005 1006 1013 1017 1024 -1.408259
## 98 1005 1006 1014 1017 1023 -1.404935
## 99 1003 1007 1014 1020 1021 -1.390486
## 100 1005 1007 1013 1016 1024 -1.364311
## 101 1004 1007 1011 1020 1023 -1.362773
## 102 1002 1010 1013 1016 1024 -1.362712
## 103 1002 1010 1014 1016 1023 -1.357470
## 104 1005 1006 1014 1018 1022 -1.356888
## 105 1002 1010 1014 1018 1021 -1.346987
## 106 1005 1007 1014 1016 1023 -1.334623
## 107 1005 1006 1013 1019 1022 -1.333759
## 108 1002 1006 1013 1019 1025 -1.329268
## 109 1005 1007 1014 1018 1021 -1.321908
## 110 1002 1009 1013 1020 1021 -1.312449
## 111 1002 1010 1013 1019 1021 -1.310664
## 112 1002 1006 1014 1020 1023 -1.307705
## 113 1002 1006 1013 1020 1024 -1.290937
## 114 1005 1007 1013 1019 1021 -1.285206
## 115 1004 1010 1013 1016 1022 -1.110151
## 116 1004 1010 1013 1017 1021 -1.105946
## 117 1004 1006 1013 1017 1025 -1.104419
## 118 1004 1007 1013 1016 1025 -1.053338
## 119 1004 1006 1013 1020 1022 -1.042303
## 120 1004 1007 1013 1020 1021 -0.990200MM
metaecosystem_type_selected = c("Medium-Medium")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
# --- FILTER DATA --- #
filtered_data = ds_metaecosystems %>%
filter(time_point %in% time_points_model,
metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym("total_water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.metaecos.points(filtered_data,
metaecosystem_type_selected,
connection_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). We also include the total water that was added due to evaporation in the microwave and the time point before the first disturbance (baseline). In the syntax of lmer4 the three models look this this:
Full model = response_variable ~connection * scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Reduced model = response_variable ~connection + scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Null model = response_variable ~scale(day) + scale(total_water_addition_ml) * scale(day) + scale(baseline) * scale(day) + (day | system_nr)
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the median of such distributions.
Code we used to computed the p-values
# --- ADD BASELINES --- #
baselines = ds_metaecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(system_nr,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PREPARE TO COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_selected,
metaecosystem_type %in% metaecosystem_type_selected)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)# --- COMPARE FULL, REDUCED, AND NULL MODEL WHILE RESHUFFLING ECOSYSTEM COMBINATIONS --- #
for (set_i in 1:n_sets) {
# Filter the data to contain all the connected meta-ecosystems and only a subset of unconnected meta-ecosystems
system_nr_unconnected_systems_selected = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
connection == "unconnected",
set == set_i) %>%
pull(system_nr)
filtered_data_2 = filtered_data %>%
filter(connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_selected))
# Construct models
full_model = try.different.optimizer.full.model()
reduced_model = try.different.optimizer.reduced.model()
null_model = try.different.optimizer.null.model()
# If all the optimisers fail, move on to the next iteration
if (is.null(full_model) || is.null(reduced_model) || is.null(null_model)) {
cat("This model could not be fitted with any optimiser. The unconnected meta-ecosystems in this iteration were:",
system_nr_unconnected_systems_selected,
"\n")
next
}
if(plot_model_residuals_metaecos == TRUE){
# Plot residuals - full model
print(qqnorm(resid(full_model))); print(qqline(resid(full_model)))
#full_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, full_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_full_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - reduced model
print(qqnorm(resid(reduced_model))); print(qqline(resid(reduced_model)))
#reduced_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, reduced_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_reduced_model.png")),
plot = plot,
width = 8,
height = 6)
# Plot residuals - null model
print(qqnorm(resid(null_model))); print(qqline(resid(null_model)))
#null_model_res_vs_fit[[set_i]] = create.res.vs.fit.metaecos(filtered_data_2, null_model)
plot = filtered_data_2 %>%
mutate(predicted = fitted(null_model),
residuals = resid(null_model)) %>%
ggplot(aes(x = predicted,
y = residuals)) +
geom_point()
ggsave(here("6_results",
"residual_plots",
paste0(disturbance_global_selected,
"_disturbance_",
gsub(pattern = " ", replacement = "", metaecosystem_type_selected[[1]]),
"_",
response_variable_selected,
"_",
set_i,
"_null_model.png")),
plot = plot,
width = 8,
height = 6)
}
# Give model statistics
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
# Save model statistics
iterated_results_table = fill.results.table(iterated_results_table,
response_variable_selected,
metaecosystem_type_selected,
model_stats_full,
model_stats_reduced)
iterated_results_table$set[nrow(iterated_results_table)] = set_i
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_selected, collapse = " ")
}## [1] "Model successfully fitted with optimizer: bobyqa "
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Full vs null model
P-value of the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_full),
p_value = median(iterated_results_table$p_full),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -1.5 0.063 * weakΔAIC and p-value distributions of the comparison between full and null models
# --- FULL VS NULL MODEL - SHOW ΔAIC & P VALUE DISTRIBUTIONS --- #
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- FULL VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1050 1055 -3.3008508
## 2 1055 1050 -3.3008508
## 3 1048 1050 -2.4229375
## 4 1050 1048 -2.4229375
## 5 1051 1054 -2.2350516
## 6 1054 1051 -2.2350516
## 7 1052 1053 -1.9741663
## 8 1053 1052 -1.9741663
## 9 1048 1052 -1.6944652
## 10 1052 1048 -1.6944652
## 11 1049 1050 -1.5989419
## 12 1050 1049 -1.5989419
## 13 1046 1055 -1.5320382
## 14 1055 1046 -1.5320382
## 15 1049 1051 -1.5179048
## 16 1051 1049 -1.5179048
## 17 1047 1051 -1.3170137
## 18 1051 1047 -1.3170137
## 19 1046 1053 -1.0203738
## 20 1053 1046 -1.0203738
## 21 1047 1052 -0.7897137
## 22 1052 1047 -0.7897137
## 23 1046 1054 -0.6788248
## 24 1054 1046 -0.6788248
## 25 1047 1055 -0.6405515
## 26 1055 1047 -0.6405515
## 27 1048 1054 -0.6336421
## 28 1054 1048 -0.6336421
## 29 1049 1053 -0.3993607
## 30 1053 1049 -0.3993607
Reduced vs null model
ΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
data.frame(deltaAIC = median(iterated_results_table$ΔAIC_fix),
p_value = median(iterated_results_table$p_fix),
R2 = NA) %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.9 0.302 noneΔAIC and p-value distributions of the comparison between reduced and null models
# --- REDUCED VS NULL MODEL - SHOW ΔAIC & P VALUE --- #
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
# --- REDUCED VS NULL MODEL - SHOW WHICH UNCONNECTED META-ECOSYSTEM NUMBER PRODUCD WHICH AIC --- #
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1050 1055 -0.08519968
## 2 1055 1050 -0.08519968
## 3 1051 1054 0.23007970
## 4 1054 1051 0.23007970
## 5 1052 1053 0.29774862
## 6 1053 1052 0.29774862
## 7 1048 1050 0.43118230
## 8 1050 1048 0.43118230
## 9 1047 1051 0.66001146
## 10 1051 1047 0.66001146
## 11 1049 1050 0.67529114
## 12 1050 1049 0.67529114
## 13 1046 1053 0.82200249
## 14 1053 1046 0.82200249
## 15 1048 1052 0.93568316
## 16 1052 1048 0.93568316
## 17 1049 1051 0.98144359
## 18 1051 1049 0.98144359
## 19 1046 1055 1.01203992
## 20 1055 1046 1.01203992
## 21 1046 1054 1.02180928
## 22 1054 1046 1.02180928
## 23 1047 1052 1.14625730
## 24 1052 1047 1.14625730
## 25 1048 1054 1.22660330
## 26 1054 1048 1.22660330
## 27 1049 1053 1.26054998
## 28 1053 1049 1.26054998
## 29 1047 1055 1.30516701
## 30 1055 1047 1.30516701All ecosystems
ecosystem_type_selected = c("Small unconnected",
"Medium unconnected",
"Large unconnected",
"Small connected to small",
"Small connected to large",
"Medium connected to medium",
"Large connected to small",
"Large connected to large")BEF
ds_ecosystems %>%
filter(is.na(species_richness) != TRUE) %>%
ggplot(aes(x = species_richness,
y = bioarea_mm2_per_ml)) +
geom_point() +
xlim(0, length(protist_species)) +
labs(x = axis_names$axis_name[axis_names$variable == "species_richness"],
y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"))
ds_ecosystems %>%
filter(is.na(shannon) != TRUE) %>%
ggplot(aes(x = shannon,
y = bioarea_mm2_per_ml)) +
geom_point() +
labs(x = axis_names$axis_name[axis_names$variable == "shannon"],
y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"))
ds_ecosystems %>%
filter(is.na(evenness_pielou) != TRUE) %>%
ggplot(aes(x = evenness_pielou,
y = bioarea_mm2_per_ml)) +
geom_point() +
labs(x = axis_names$axis_name[axis_names$variable == "evenness_pielou"],
y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"))
Evaporation (both disturbance levels)
response_variable_selected = "water_addition_ml"UNLIKE ALL THE OTHER ANALYSIS, THIS INCLUDES BOTH DISTURBANCE LEVELS.
We want to know whether the size of an ecosystem influenced its evaporation rate. We first start from plotting how the water that was added to the cultures changed across size through its mean ± 95 confidence interval:
# --- FILTER DATASET --- #
ds_ecosystems_both_disturbances_filtered = ds_ecosystems_both_disturbances %>%
filter(!is.na(water_addition_ml)) %>%
mutate(sqrt_water_addition_ml = sqrt(water_addition_ml),
log_water_addition_ml = log(water_addition_ml),
inv_water_addition_ml = 1 / water_addition_ml)# --- PLOT WATER ADDITION MEAN ± 95 CI --- #
ds_ecosystems_both_disturbances_filtered %>%
summarySE(measurevar = response_variable_selected,
groupvars = c("day", "ecosystem_size")) %>%
ggplot(aes(x = day,
y = get(response_variable_selected),
group = interaction(day, ecosystem_size),
color = ecosystem_size)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_size),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
ymin = get(response_variable_selected) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = "Day",
y = "Water addition (ml)",
color = "") +
scale_x_continuous(breaks = unique(ds_ecosystems$day)) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position) +
scale_color_manual(values = c("#000000", "#737373", "#bdbdbd")) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
Single replicates
# --- PLOT WATER ADDITION SINGLE REPLICATES --- #
ds_ecosystems_both_disturbances_filtered %>%
ggplot(aes(x = day,
y = get(response_variable_selected),
group = interaction(culture_ID, day),
color = ecosystem_size)) +
geom_point() +
geom_line(aes(group = culture_ID)) +
scale_x_continuous(breaks = unique(ds_ecosystems$day)) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color) +
labs(x = "Day",
y = "Water addition (ml)",
color = "") +
scale_color_manual(values = c("#000000", "#737373", "#bdbdbd"))
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size +
(1 | time_point),
data = ds_ecosystems_both_disturbances_filtered,
REML = FALSE)
null_model = lmer(get(response_variable_selected) ~
(1 | time_point),
data = ds_ecosystems_both_disturbances_filtered,
REML = FALSE)Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
print()## deltaAIC p_value R2
## 1 -4.690089 0.01297093 NAFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + (1 | time_point)
## Data: ds_ecosystems_both_disturbances_filtered
##
## AIC BIC logLik deviance df.resid
## 748.4 769.9 -369.2 738.4 538
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8 -0.7 0.1 0.4 4.5
##
## Random effects:
## Groups Name Variance Std.Dev.
## time_point (Intercept) 0.2 0.4
## Residual 0.2 0.5
## Number of obs: 543, groups: time_point, 5
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.63 0.20 5.18 8 4e-04 ***
## ecosystem_sizeMedium -0.13 0.05 538.00 -3 0.009 **
## ecosystem_sizeSmall -0.12 0.05 538.00 -2 0.015 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M
## ecsystm_szM -0.109
## ecsystm_szS -0.117 0.459Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(ds_ecosystems_both_disturbances_filtered, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT MEAN ± 95% CI --- #
"High disturbance"## [1] "High disturbance"plot.all.patches.points(data = ds_ecosystems_both_disturbances %>% filter(disturbance == "high"),
response_variable_selected)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
"Low disturbance"## [1] "Low disturbance"plot.all.patches.points(data = ds_ecosystems_both_disturbances %>% filter(disturbance == "low"),
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. To do so, we go through the following steps.
- Add baseline level of this response variable (time point 1) to the cultures.
- Filter the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, the time points preceding the initial disturbance and resource flow, and the last time point which we are not including because we do not know how much water evaporated previously from the water addition.
- Plot the data to make sure that what filtered in the right way.
- Develop mixed effect models to examine how ecosystem type influenced this variable.
# --- ADD BASELINES --- #
baselines = ds_ecosystems_both_disturbances %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
data_for_analysis = ds_ecosystems_both_disturbances %>%
left_join(baselines)# --- FILTER DATA AND CHANGE THE NAME OF LEVELS --- #
data_for_analysis = data_for_analysis %>%
filter(time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(water_addition_ml)) %>%
mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
ecosystem_type == "Medium unconnected" ~ "M",
ecosystem_type == "Large unconnected" ~ "L",
ecosystem_type == "Small connected to small" ~ "S_S",
ecosystem_type == "Small connected to large" ~ "S_L",
ecosystem_type == "Medium connected to medium" ~ "M_M",
ecosystem_type == "Large connected to large" ~ "L_L",
ecosystem_type == "Large connected to small" ~ "L_S",
TRUE ~ ecosystem_type))# --- ADD EVAPORATION RATES RESIDUALS --- #
evaporation_model = lm(get(response_variable_selected) ~
ecosystem_type * disturbance * day +
baseline * day,
data = data_for_analysis)
par(mfrow = c(2, 2))
plot(evaporation_model)
data_for_analysis = data_for_analysis %>%
mutate(evaporation_residuals = residuals(evaporation_model))# --- PLOT MEAN ± 95% CI OF FILTERED DATA --- #
"High disturbance"## [1] "High disturbance"plot.all.patches.points(data = data_for_analysis %>% filter(disturbance == "high"),
response_variable_selected)
"Low disturbance"## [1] "Low disturbance"plot.all.patches.points(data = data_for_analysis %>% filter(disturbance == "low"),
response_variable_selected)
# --- CHECK COLLINEARITY --- #
# # Select the relevant numeric columns (ensure that they are numeric)
# numeric_data <- data_for_analysis %>%
# select(day, water_addition_ml, baseline)
#
# # Calculate the correlation matrix
# cor_matrix <- cor(numeric_data, use = "complete.obs")
#
# # Use corrplot to visualize the correlation matrix
# corrplot::corrplot(cor_matrix, method = 'number')# --- CONSTRUCT MODEL --- #
# full_model = lmer(get(response_variable_selected) ~
# ecosystem_type * disturbance * day +
# water_addition_ml * day +
# baseline * day +
# (day | culture_ID),
# data = data_for_analysis,
# REML = FALSE)
full_model <- glmmTMB(get(response_variable_selected) ~
ecosystem_type * disturbance * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = data_for_analysis,
family = tweedie(link = "log"),
control = glmmTMBControl(optimizer = "optim"))## Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old): Model convergence
## problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')## Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old): Model convergence
## problem; . See vignette('troubleshooting'), help('diagnose')# --- SHOW MODEL SUMMARY --- #
print(summary(full_model), digits = 1)## Warning in sqrt(diag(vcovs)): NaNs produced## Family: tweedie ( log )
## Formula:
## get(response_variable_selected) ~ ecosystem_type * disturbance *
## scale(day) + scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: data_for_analysis
##
## AIC BIC logLik deviance df.resid
## NA NA NA NA 489
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.7 0.8
## day 0.7 0.9 0.17
## Number of obs: 530, groups: culture_ID, 109
##
## Dispersion parameter for tweedie family (): 0.459
##
## Conditional model:
## Estimate Std. Error z value
## (Intercept) 0.049 7.726 0.0
## ecosystem_typeL_L 0.070 9.375 0.0
## ecosystem_typeL_S 0.008 10.807 0.0
## ecosystem_typeM 0.020 10.890 0.0
## ecosystem_typeM_M 0.065 9.342 0.0
## ecosystem_typeS 0.066 NaN NaN
## ecosystem_typeS_L 0.069 6.705 0.0
## ecosystem_typeS_S 0.064 NaN NaN
## disturbancelow 0.071 10.658 0.0
## scale(day) -0.010 2.172 0.0
## scale(water_addition_ml) 0.056 0.051 1.1
## scale(baseline) 0.054 1.381 0.0
## ecosystem_typeL_L:disturbancelow 0.061 13.222 0.0
## ecosystem_typeL_S:disturbancelow 0.138 15.089 0.0
## ecosystem_typeM:disturbancelow -0.026 14.632 0.0
## ecosystem_typeM_M:disturbancelow 0.024 12.999 0.0
## ecosystem_typeS:disturbancelow 0.049 1.436 0.0
## ecosystem_typeS_L:disturbancelow -0.105 11.318 0.0
## ecosystem_typeS_S:disturbancelow 0.056 10.417 0.0
## ecosystem_typeL_L:scale(day) 0.035 2.636 0.0
## ecosystem_typeL_S:scale(day) -0.022 3.039 0.0
## ecosystem_typeM:scale(day) -0.039 3.062 0.0
## ecosystem_typeM_M:scale(day) 0.039 2.627 0.0
## ecosystem_typeS:scale(day) 0.070 NaN NaN
## ecosystem_typeS_L:scale(day) 0.040 1.868 0.0
## ecosystem_typeS_S:scale(day) -0.055 NaN NaN
## disturbancelow:scale(day) -0.013 2.996 0.0
## scale(day):scale(water_addition_ml) 0.020 0.047 0.4
## scale(day):scale(baseline) 0.059 0.386 0.2
## ecosystem_typeL_L:disturbancelow:scale(day) 0.074 3.718 0.0
## ecosystem_typeL_S:disturbancelow:scale(day) -0.008 4.241 0.0
## ecosystem_typeM:disturbancelow:scale(day) 0.031 4.111 0.0
## ecosystem_typeM_M:disturbancelow:scale(day) 0.031 3.654 0.0
## ecosystem_typeS:disturbancelow:scale(day) 0.044 0.774 0.1
## ecosystem_typeS_L:disturbancelow:scale(day) -0.059 3.167 0.0
## ecosystem_typeS_S:disturbancelow:scale(day) 0.064 2.922 0.0
## Pr(>|z|)
## (Intercept) 1.0
## ecosystem_typeL_L 1.0
## ecosystem_typeL_S 1.0
## ecosystem_typeM 1.0
## ecosystem_typeM_M 1.0
## ecosystem_typeS NaN
## ecosystem_typeS_L 1.0
## ecosystem_typeS_S NaN
## disturbancelow 1.0
## scale(day) 1.0
## scale(water_addition_ml) 0.3
## scale(baseline) 1.0
## ecosystem_typeL_L:disturbancelow 1.0
## ecosystem_typeL_S:disturbancelow 1.0
## ecosystem_typeM:disturbancelow 1.0
## ecosystem_typeM_M:disturbancelow 1.0
## ecosystem_typeS:disturbancelow 1.0
## ecosystem_typeS_L:disturbancelow 1.0
## ecosystem_typeS_S:disturbancelow 1.0
## ecosystem_typeL_L:scale(day) 1.0
## ecosystem_typeL_S:scale(day) 1.0
## ecosystem_typeM:scale(day) 1.0
## ecosystem_typeM_M:scale(day) 1.0
## ecosystem_typeS:scale(day) NaN
## ecosystem_typeS_L:scale(day) 1.0
## ecosystem_typeS_S:scale(day) NaN
## disturbancelow:scale(day) 1.0
## scale(day):scale(water_addition_ml) 0.7
## scale(day):scale(baseline) 0.9
## ecosystem_typeL_L:disturbancelow:scale(day) 1.0
## ecosystem_typeL_S:disturbancelow:scale(day) 1.0
## ecosystem_typeM:disturbancelow:scale(day) 1.0
## ecosystem_typeM_M:disturbancelow:scale(day) 1.0
## ecosystem_typeS:disturbancelow:scale(day) 1.0
## ecosystem_typeS_L:disturbancelow:scale(day) 1.0
## ecosystem_typeS_S:disturbancelow:scale(day) 1.0# --- RUN ANOVA --- #
car::Anova(full_model, type = "III")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: get(response_variable_selected)
## Chisq Df Pr(>Chisq)
## (Intercept) 0.0000 1 0.9949
## ecosystem_type 0.0001 7 1.0000
## disturbance 0.0000 1 0.9947
## scale(day) 0.0000 1 0.9962
## scale(water_addition_ml) 1.2133 1 0.2707
## scale(baseline) 0.0015 1 0.9688
## ecosystem_type:disturbance 0.0003 7 1.0000
## ecosystem_type:scale(day) 0.0039 7 1.0000
## disturbance:scale(day) 0.0000 1 0.9966
## scale(day):scale(water_addition_ml) 0.1868 1 0.6656
## scale(day):scale(baseline) 0.0231 1 0.8792
## ecosystem_type:disturbance:scale(day) 0.0017 7 1.0000Model contrast coding
# --- GET ECOSYSTEM TYPE CONSTRASTS --- #
emmeans_output = emmeans(full_model,
specs = pairwise ~ ecosystem_type * disturbance,
adjust = "tukey",
bias.adj = TRUE,
lmer.df = "satterthwaite")
emmeans_output## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!
## Warning in .qf.non0(object@V, x): Negative variance estimate obtained!## $emmeans
## ecosystem_type disturbance emmean SE df asymp.LCL asymp.UCL
## L high 0.0494 7.73 Inf -15.09 15.19
## L_L high 0.1197 5.42 Inf -10.51 10.75
## L_S high 0.0570 7.66 Inf -14.96 15.07
## M high 0.0690 7.66 Inf -14.94 15.07
## M_M high 0.1145 5.48 Inf -10.62 10.85
## S high 0.1157 NaN Inf NaN NaN
## S_L high 0.1182 NaN Inf NaN NaN
## S_S high 0.1130 NaN Inf NaN NaN
## L low 0.1203 7.64 Inf -14.84 15.08
## L_L low 0.2520 5.32 Inf -10.17 10.67
## L_S low 0.2662 7.25 Inf -13.95 14.48
## M low 0.1137 7.20 Inf -14.01 14.23
## M_M low 0.2096 5.48 Inf -10.54 10.96
## S low 0.2361 5.42 Inf -10.38 10.85
## S_L low 0.0839 7.80 Inf -15.21 15.38
## S_S low 0.2395 4.20 Inf -7.99 8.47
##
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L high - L_L high -0.070344 9.38 Inf -0.008 1.0000
## L high - L_S high -0.007617 10.81 Inf -0.001 1.0000
## L high - M high -0.019654 10.89 Inf -0.002 1.0000
## L high - M_M high -0.065118 9.34 Inf -0.007 1.0000
## L high - S high -0.066334 NaN Inf NaN NaN
## L high - S_L high -0.068784 6.70 Inf -0.010 1.0000
## L high - S_S high -0.063653 NaN Inf NaN NaN
## L high - L low -0.070903 10.66 Inf -0.007 1.0000
## L high - L_L low -0.202587 9.26 Inf -0.022 1.0000
## L high - L_S low -0.216819 10.78 Inf -0.020 1.0000
## L high - M low -0.064341 10.67 Inf -0.006 1.0000
## L high - M_M low -0.160174 9.38 Inf -0.017 1.0000
## L high - S low -0.186673 9.20 Inf -0.020 1.0000
## L high - S_L low -0.034558 11.15 Inf -0.003 1.0000
## L high - S_S low -0.190097 8.53 Inf -0.022 1.0000
## L_L high - L_S high 0.062727 9.30 Inf 0.007 1.0000
## L_L high - M high 0.050689 9.39 Inf 0.005 1.0000
## L_L high - M_M high 0.005226 7.67 Inf 0.001 1.0000
## L_L high - S high 0.004010 NaN Inf NaN NaN
## L_L high - S_L high 0.001559 5.01 Inf 0.000 1.0000
## L_L high - S_S high 0.006691 NaN Inf NaN NaN
## L_L high - L low -0.000559 9.34 Inf 0.000 1.0000
## L_L high - L_L low -0.132243 7.61 Inf -0.017 1.0000
## L_L high - L_S low -0.146475 9.02 Inf -0.016 1.0000
## L_L high - M low 0.006003 8.94 Inf 0.001 1.0000
## L_L high - M_M low -0.089830 7.65 Inf -0.012 1.0000
## L_L high - S low -0.116329 7.86 Inf -0.015 1.0000
## L_L high - S_L low 0.035785 9.59 Inf 0.004 1.0000
## L_L high - S_S low -0.119753 6.94 Inf -0.017 1.0000
## L_S high - M high -0.012038 10.84 Inf -0.001 1.0000
## L_S high - M_M high -0.057501 9.26 Inf -0.006 1.0000
## L_S high - S high -0.058717 NaN Inf NaN NaN
## L_S high - S_L high -0.061168 5.71 Inf -0.011 1.0000
## L_S high - S_S high -0.056036 NaN Inf NaN NaN
## L_S high - L low -0.063286 10.51 Inf -0.006 1.0000
## L_S high - L_L low -0.194970 9.12 Inf -0.021 1.0000
## L_S high - L_S low -0.209202 10.89 Inf -0.019 1.0000
## L_S high - M low -0.056724 10.79 Inf -0.005 1.0000
## L_S high - M_M low -0.152557 9.34 Inf -0.016 1.0000
## L_S high - S low -0.179056 8.74 Inf -0.020 1.0000
## L_S high - S_L low -0.026942 11.11 Inf -0.002 1.0000
## L_S high - S_S low -0.182480 8.19 Inf -0.022 1.0000
## M high - M_M high -0.045463 9.43 Inf -0.005 1.0000
## M high - S high -0.046679 NaN Inf NaN NaN
## M high - S_L high -0.049130 6.98 Inf -0.007 1.0000
## M high - S_S high -0.043998 NaN Inf NaN NaN
## M high - L low -0.051249 10.83 Inf -0.005 1.0000
## M high - L_L low -0.182933 9.33 Inf -0.020 1.0000
## M high - L_S low -0.197165 10.54 Inf -0.019 1.0000
## M high - M low -0.044687 10.52 Inf -0.004 1.0000
## M high - M_M low -0.140520 9.43 Inf -0.015 1.0000
## M high - S low -0.167018 9.36 Inf -0.018 1.0000
## M high - S_L low -0.014904 10.93 Inf -0.001 1.0000
## M high - S_S low -0.170442 8.73 Inf -0.020 1.0000
## M_M high - S high -0.001216 NaN Inf NaN NaN
## M_M high - S_L high -0.003667 5.38 Inf -0.001 1.0000
## M_M high - S_S high 0.001465 NaN Inf NaN NaN
## M_M high - L low -0.005785 9.33 Inf -0.001 1.0000
## M_M high - L_L low -0.137469 7.63 Inf -0.018 1.0000
## M_M high - L_S low -0.151701 9.05 Inf -0.017 1.0000
## M_M high - M low 0.000777 8.93 Inf 0.000 1.0000
## M_M high - M_M low -0.095056 7.62 Inf -0.012 1.0000
## M_M high - S low -0.121555 8.01 Inf -0.015 1.0000
## M_M high - S_L low 0.030559 9.69 Inf 0.003 1.0000
## M_M high - S_S low -0.124979 7.01 Inf -0.018 1.0000
## S high - S_L high -0.002451 4.43 Inf -0.001 1.0000
## S high - S_S high 0.002681 3.90 Inf 0.001 1.0000
## S high - L low -0.004569 NaN Inf NaN NaN
## S high - L_L low -0.136253 NaN Inf NaN NaN
## S high - L_S low -0.150485 NaN Inf NaN NaN
## S high - M low 0.001993 NaN Inf NaN NaN
## S high - M_M low -0.093840 NaN Inf NaN NaN
## S high - S low -0.120339 NaN Inf NaN NaN
## S high - S_L low 0.031775 NaN Inf NaN NaN
## S high - S_S low -0.123763 NaN Inf NaN NaN
## S_L high - S_S high 0.005132 9.33 Inf 0.001 1.0000
## S_L high - L low -0.002119 8.73 Inf 0.000 1.0000
## S_L high - L_L low -0.133802 6.22 Inf -0.022 1.0000
## S_L high - L_S low -0.148035 NaN Inf NaN NaN
## S_L high - M low 0.004444 NaN Inf NaN NaN
## S_L high - M_M low -0.091390 4.17 Inf -0.022 1.0000
## S_L high - S low -0.117888 10.46 Inf -0.011 1.0000
## S_L high - S_L low 0.034226 6.83 Inf 0.005 1.0000
## S_L high - S_S low -0.121312 8.18 Inf -0.015 1.0000
## S_S high - L low -0.007250 4.54 Inf -0.002 1.0000
## S_S high - L_L low -0.138934 NaN Inf NaN NaN
## S_S high - L_S low -0.153166 NaN Inf NaN NaN
## S_S high - M low -0.000688 NaN Inf NaN NaN
## S_S high - M_M low -0.096521 NaN Inf NaN NaN
## S_S high - S low -0.123020 8.33 Inf -0.015 1.0000
## S_S high - S_L low 0.029095 NaN Inf NaN NaN
## S_S high - S_S low -0.126444 4.40 Inf -0.029 1.0000
## L low - L_L low -0.131684 9.41 Inf -0.014 1.0000
## L low - L_S low -0.145916 10.26 Inf -0.014 1.0000
## L low - M low 0.006562 10.12 Inf 0.001 1.0000
## L low - M_M low -0.089271 9.21 Inf -0.010 1.0000
## L low - S low -0.115770 10.22 Inf -0.011 1.0000
## L low - S_L low 0.036345 11.11 Inf 0.003 1.0000
## L low - S_S low -0.119194 9.19 Inf -0.013 1.0000
## L_L low - L_S low -0.014232 8.70 Inf -0.002 1.0000
## L_L low - M low 0.138246 8.62 Inf 0.016 1.0000
## L_L low - M_M low 0.042413 7.53 Inf 0.006 1.0000
## L_L low - S low 0.015914 8.38 Inf 0.002 1.0000
## L_L low - S_L low 0.168029 9.52 Inf 0.018 1.0000
## L_L low - S_S low 0.012490 7.29 Inf 0.002 1.0000
## L_S low - M low 0.152478 10.85 Inf 0.014 1.0000
## L_S low - M_M low 0.056645 9.25 Inf 0.006 1.0000
## L_S low - S low 0.030146 7.35 Inf 0.004 1.0000
## L_S low - S_L low 0.182261 10.58 Inf 0.017 1.0000
## L_S low - S_S low 0.026722 7.31 Inf 0.004 1.0000
## M low - M_M low -0.095833 9.14 Inf -0.010 1.0000
## M low - S low -0.122332 7.29 Inf -0.017 1.0000
## M low - S_L low 0.029783 10.65 Inf 0.003 1.0000
## M low - S_S low -0.125756 7.18 Inf -0.018 1.0000
## M_M low - S low -0.026499 7.53 Inf -0.004 1.0000
## M_M low - S_L low 0.125616 9.69 Inf 0.013 1.0000
## M_M low - S_S low -0.029923 6.67 Inf -0.004 1.0000
## S low - S_L low 0.152114 9.39 Inf 0.016 1.0000
## S low - S_S low -0.003424 9.21 Inf 0.000 1.0000
## S_L low - S_S low -0.155538 8.92 Inf -0.017 1.0000
##
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 14.2931142241337 estimateshigh_L = c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_L_L = c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_L_S = c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_M = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_M_M = c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_S = c(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_S_L = c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_S_S = c(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
n_of_digits = 3
contrasts = contrast(emmeans_output,
method = list("high S_L - S" = high_S_L - high_S,
"high S_L - S_S" = high_S_L - high_S_S,
"high S_S - S" = high_S_S - high_S,
"high M_M - M" = high_M_M - high_M,
"high L_S - L" = high_L_S - high_L,
"high L_S - L_L" = high_L_S - high_L_L,
"high L_L - L" = high_L_L - high_L,
"low S_L - S" = low_S_L - low_S,
"low S_L - S_S" = low_S_L - low_S_S,
"low S_S - S" = low_S_S - low_S,
"low M_M - M" = low_M_M - low_M,
"low L_S - L" = low_L_S - low_L,
"low L_S - L_L" = low_L_S - low_L_L,
"low L_L - L" = low_L_L - low_L)) %>%
as.data.frame() %>%
mutate(p.value = round(p.value, digits = n_of_digits),
estimate = round(estimate, digits = n_of_digits),
SE = round(SE, digits = n_of_digits),
df = round(df, digits = n_of_digits),
z.ratio = round(z.ratio, digits = n_of_digits),
e = "",
e = ifelse(p.value > 0.1,
"",
e),
e = ifelse(p.value < 0.05,
"*",
e),
e = ifelse(p.value < 0.01,
"**",
e),
e = ifelse(p.value < 0.001,
"***",
e)) %>%
rename(" " = e)# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #
contrasts## contrast estimate SE df z.ratio p.value
## 1 high S_L - S 0.002 4.430 Inf 0.001 1.000
## 2 high S_L - S_S 0.005 9.331 Inf 0.001 1.000
## 3 high S_S - S -0.003 3.899 Inf -0.001 0.999
## 4 high M_M - M 0.045 9.425 Inf 0.005 0.996
## 5 high L_S - L 0.008 10.807 Inf 0.001 0.999
## 6 high L_S - L_L -0.063 9.298 Inf -0.007 0.995
## 7 high L_L - L 0.070 9.375 Inf 0.008 0.994
## 8 low S_L - S -0.152 9.389 Inf -0.016 0.987
## 9 low S_L - S_S -0.156 8.917 Inf -0.017 0.986
## 10 low S_S - S 0.003 9.214 Inf 0.000 1.000
## 11 low M_M - M 0.096 9.139 Inf 0.010 0.992
## 12 low L_S - L 0.146 10.257 Inf 0.014 0.989
## 13 low L_S - L_L 0.014 8.703 Inf 0.002 0.999
## 14 low L_L - L 0.132 9.413 Inf 0.014 0.989# --- CONSTRUCT RESIDUALS VS FITTED VALUES PLOT --- #
res_vs_fit = data_for_analysis %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
data_for_analysis$culture_ID,
"<br>",
"Day: ",
data_for_analysis$day,
"<br>",
"Patch Type: ",
data_for_analysis$ecosystem_type,
"<br>",
"Biomass density: ",
round(data_for_analysis$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
data_for_analysis$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))# --- PLOT RESIDUALS --- #
qqnorm(resid(full_model))
qqline(resid(full_model))
res_vs_fitBiomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT MEAN ± 95% CI --- #
"High disturbance"## [1] "High disturbance"plot.all.patches.points(data = ds_ecosystems_both_disturbances %>% filter(disturbance == "high"),
response_variable_selected)
"Low disturbance"## [1] "Low disturbance"plot.all.patches.points(data = ds_ecosystems_both_disturbances %>% filter(disturbance == "low"),
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. To do so, we go through the following steps.
- Add baseline level of this response variable (time point 1) to the cultures.
- Filter the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, the time points preceding the initial disturbance and resource flow, and the last time point which we are not including because we do not know how much water evaporated previously from the water addition.
- Plot the data to make sure that what filtered in the right way.
- Develop mixed effect models to examine how ecosystem type influenced this variable.
# --- ADD BASELINES --- #
baselines = ds_ecosystems_both_disturbances %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
data_for_analysis = ds_ecosystems_both_disturbances %>%
left_join(baselines)# --- FILTER DATA AND CHANGE THE NAME OF LEVELS --- #
data_for_analysis = data_for_analysis %>%
filter(time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(water_addition_ml)) %>%
mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
ecosystem_type == "Medium unconnected" ~ "M",
ecosystem_type == "Large unconnected" ~ "L",
ecosystem_type == "Small connected to small" ~ "S_S",
ecosystem_type == "Small connected to large" ~ "S_L",
ecosystem_type == "Medium connected to medium" ~ "M_M",
ecosystem_type == "Large connected to large" ~ "L_L",
ecosystem_type == "Large connected to small" ~ "L_S",
TRUE ~ ecosystem_type))# --- ADD EVAPORATION RATES RESIDUALS --- #
evaporation_model = lm(get(response_variable_selected) ~
ecosystem_type * disturbance * day +
baseline * day,
data = data_for_analysis)
par(mfrow = c(2, 2))
plot(evaporation_model)
data_for_analysis = data_for_analysis %>%
mutate(evaporation_residuals = residuals(evaporation_model))# --- PLOT MEAN ± 95% CI OF FILTERED DATA --- #
"High disturbance"## [1] "High disturbance"plot.all.patches.points(data = data_for_analysis %>% filter(disturbance == "high"),
response_variable_selected)
"Low disturbance"## [1] "Low disturbance"plot.all.patches.points(data = data_for_analysis %>% filter(disturbance == "low"),
response_variable_selected)
# --- CHECK COLLINEARITY --- #
# # Select the relevant numeric columns (ensure that they are numeric)
# numeric_data <- data_for_analysis %>%
# select(day, water_addition_ml, baseline)
#
# # Calculate the correlation matrix
# cor_matrix <- cor(numeric_data, use = "complete.obs")
#
# # Use corrplot to visualize the correlation matrix
# corrplot::corrplot(cor_matrix, method = 'number')# --- CONSTRUCT MODEL --- #
# full_model = lmer(get(response_variable_selected) ~
# ecosystem_type * disturbance * day +
# water_addition_ml * day +
# baseline * day +
# (day | culture_ID),
# data = data_for_analysis,
# REML = FALSE)
full_model <- glmmTMB(get(response_variable_selected) ~
ecosystem_type * disturbance * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = data_for_analysis,
family = tweedie(link = "log"),
control = glmmTMBControl(optimizer = "optim"))## Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old): Model convergence
## problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')## Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old): Model convergence
## problem; . See vignette('troubleshooting'), help('diagnose')# --- SHOW MODEL SUMMARY --- #
print(summary(full_model), digits = 1)## Family: tweedie ( log )
## Formula:
## get(response_variable_selected) ~ ecosystem_type * disturbance *
## scale(day) + scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: data_for_analysis
##
## AIC BIC logLik deviance df.resid
## NA NA NA NA 502
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1.0 1.0
## day 0.7 0.9 -0.05
## Number of obs: 543, groups: culture_ID, 109
##
## Dispersion parameter for tweedie family (): 0.792
##
## Conditional model:
## Estimate Std. Error z value
## (Intercept) 0.082 8.012 0.0
## ecosystem_typeL_L 0.041 9.546 0.0
## ecosystem_typeL_S 0.117 10.968 0.0
## ecosystem_typeM 0.045 11.176 0.0
## ecosystem_typeM_M 0.045 9.570 0.0
## ecosystem_typeS 0.222 18.632 0.0
## ecosystem_typeS_L 0.039 12.924 0.0
## ecosystem_typeS_S 0.033 13.141 0.0
## disturbancelow 0.122 11.559 0.0
## scale(day) -0.529 2.275 -0.2
## scale(water_addition_ml) 0.073 0.067 1.1
## scale(baseline) -0.014 1.822 0.0
## ecosystem_typeL_L:disturbancelow 0.048 13.517 0.0
## ecosystem_typeL_S:disturbancelow 0.062 15.452 0.0
## ecosystem_typeM:disturbancelow -0.026 15.808 0.0
## ecosystem_typeM_M:disturbancelow 0.034 13.507 0.0
## ecosystem_typeS:disturbancelow 0.021 16.115 0.0
## ecosystem_typeS_L:disturbancelow -0.062 15.339 0.0
## ecosystem_typeS_S:disturbancelow 0.042 13.497 0.0
## ecosystem_typeL_L:scale(day) 0.057 2.712 0.0
## ecosystem_typeL_S:scale(day) -0.006 3.116 0.0
## ecosystem_typeM:scale(day) 0.033 3.176 0.0
## ecosystem_typeM_M:scale(day) -0.022 2.719 0.0
## ecosystem_typeS:scale(day) 0.168 5.306 0.0
## ecosystem_typeS_L:scale(day) 0.185 3.674 0.1
## ecosystem_typeS_S:scale(day) 0.004 3.734 0.0
## disturbancelow:scale(day) -0.104 3.290 0.0
## scale(day):scale(water_addition_ml) -0.045 0.059 -0.8
## scale(day):scale(baseline) 0.025 0.518 0.0
## ecosystem_typeL_L:disturbancelow:scale(day) -0.128 3.841 0.0
## ecosystem_typeL_S:disturbancelow:scale(day) -0.053 4.391 0.0
## ecosystem_typeM:disturbancelow:scale(day) -0.062 4.493 0.0
## ecosystem_typeM_M:disturbancelow:scale(day) 0.008 3.839 0.0
## ecosystem_typeS:disturbancelow:scale(day) 0.041 4.592 0.0
## ecosystem_typeS_L:disturbancelow:scale(day) -0.042 4.361 0.0
## ecosystem_typeS_S:disturbancelow:scale(day) 0.029 3.839 0.0
## Pr(>|z|)
## (Intercept) 1.0
## ecosystem_typeL_L 1.0
## ecosystem_typeL_S 1.0
## ecosystem_typeM 1.0
## ecosystem_typeM_M 1.0
## ecosystem_typeS 1.0
## ecosystem_typeS_L 1.0
## ecosystem_typeS_S 1.0
## disturbancelow 1.0
## scale(day) 0.8
## scale(water_addition_ml) 0.3
## scale(baseline) 1.0
## ecosystem_typeL_L:disturbancelow 1.0
## ecosystem_typeL_S:disturbancelow 1.0
## ecosystem_typeM:disturbancelow 1.0
## ecosystem_typeM_M:disturbancelow 1.0
## ecosystem_typeS:disturbancelow 1.0
## ecosystem_typeS_L:disturbancelow 1.0
## ecosystem_typeS_S:disturbancelow 1.0
## ecosystem_typeL_L:scale(day) 1.0
## ecosystem_typeL_S:scale(day) 1.0
## ecosystem_typeM:scale(day) 1.0
## ecosystem_typeM_M:scale(day) 1.0
## ecosystem_typeS:scale(day) 1.0
## ecosystem_typeS_L:scale(day) 1.0
## ecosystem_typeS_S:scale(day) 1.0
## disturbancelow:scale(day) 1.0
## scale(day):scale(water_addition_ml) 0.4
## scale(day):scale(baseline) 1.0
## ecosystem_typeL_L:disturbancelow:scale(day) 1.0
## ecosystem_typeL_S:disturbancelow:scale(day) 1.0
## ecosystem_typeM:disturbancelow:scale(day) 1.0
## ecosystem_typeM_M:disturbancelow:scale(day) 1.0
## ecosystem_typeS:disturbancelow:scale(day) 1.0
## ecosystem_typeS_L:disturbancelow:scale(day) 1.0
## ecosystem_typeS_S:disturbancelow:scale(day) 1.0# --- RUN ANOVA --- #
car::Anova(full_model, type = "III")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: get(response_variable_selected)
## Chisq Df Pr(>Chisq)
## (Intercept) 0.0001 1 0.9919
## ecosystem_type 0.0004 7 1.0000
## disturbance 0.0001 1 0.9916
## scale(day) 0.0541 1 0.8161
## scale(water_addition_ml) 1.2106 1 0.2712
## scale(baseline) 0.0001 1 0.9940
## ecosystem_type:disturbance 0.0001 7 1.0000
## ecosystem_type:scale(day) 0.0081 7 1.0000
## disturbance:scale(day) 0.0010 1 0.9747
## scale(day):scale(water_addition_ml) 0.5918 1 0.4417
## scale(day):scale(baseline) 0.0023 1 0.9617
## ecosystem_type:disturbance:scale(day) 0.0038 7 1.0000Model contrast coding
# --- GET ECOSYSTEM TYPE CONSTRASTS --- #
emmeans_output = emmeans(full_model,
specs = pairwise ~ ecosystem_type * disturbance,
adjust = "tukey",
bias.adj = TRUE,
lmer.df = "satterthwaite")
emmeans_output## $emmeans
## ecosystem_type disturbance emmean SE df asymp.LCL asymp.UCL
## L high 0.0816 8.01 Inf -15.6 15.8
## L_L high 0.1229 5.79 Inf -11.2 11.5
## L_S high 0.1982 7.78 Inf -15.0 15.4
## M high 0.1263 7.80 Inf -15.2 15.4
## M_M high 0.1270 5.49 Inf -10.6 10.9
## S high 0.3036 15.11 Inf -29.3 29.9
## S_L high 0.1210 9.07 Inf -17.7 17.9
## S_S high 0.1144 8.82 Inf -17.2 17.4
## L low 0.2038 9.87 Inf -19.1 19.6
## L_L low 0.2927 7.77 Inf -14.9 15.5
## L_S low 0.3821 8.80 Inf -16.9 17.6
## M low 0.2222 8.34 Inf -16.1 16.6
## M_M low 0.2836 6.23 Inf -11.9 12.5
## S low 0.4465 9.33 Inf -17.8 18.7
## S_L low 0.1811 7.76 Inf -15.0 15.4
## S_S low 0.2787 6.42 Inf -12.3 12.9
##
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df z.ratio p.value
## L high - L_L high -0.041320 9.55 Inf -0.004 1.0000
## L high - L_S high -0.116634 10.97 Inf -0.011 1.0000
## L high - M high -0.044711 11.18 Inf -0.004 1.0000
## L high - M_M high -0.045352 9.57 Inf -0.005 1.0000
## L high - S high -0.221965 18.63 Inf -0.012 1.0000
## L high - S_L high -0.039397 12.92 Inf -0.003 1.0000
## L high - S_S high -0.032794 13.14 Inf -0.002 1.0000
## L high - L low -0.122230 11.56 Inf -0.011 1.0000
## L high - L_L low -0.211054 9.88 Inf -0.021 1.0000
## L high - L_S low -0.300509 10.99 Inf -0.027 1.0000
## L high - M low -0.140576 10.83 Inf -0.013 1.0000
## L high - M_M low -0.201956 9.43 Inf -0.021 1.0000
## L high - S low -0.364936 13.24 Inf -0.028 1.0000
## L high - S_L low -0.099516 11.17 Inf -0.009 1.0000
## L high - S_S low -0.197048 10.89 Inf -0.018 1.0000
## L_L high - L_S high -0.075314 9.56 Inf -0.008 1.0000
## L_L high - M high -0.003391 9.56 Inf 0.000 1.0000
## L_L high - M_M high -0.004032 7.89 Inf -0.001 1.0000
## L_L high - S high -0.180645 17.48 Inf -0.010 1.0000
## L_L high - S_L high 0.001924 11.54 Inf 0.000 1.0000
## L_L high - S_S high 0.008526 11.64 Inf 0.001 1.0000
## L_L high - L low -0.080910 10.33 Inf -0.008 1.0000
## L_L high - L_L low -0.169733 8.52 Inf -0.020 1.0000
## L_L high - L_S low -0.259189 9.73 Inf -0.027 1.0000
## L_L high - M low -0.099256 9.62 Inf -0.010 1.0000
## L_L high - M_M low -0.160636 7.92 Inf -0.020 1.0000
## L_L high - S low -0.323616 11.72 Inf -0.028 1.0000
## L_L high - S_L low -0.058196 9.58 Inf -0.006 1.0000
## L_L high - S_S low -0.155728 9.38 Inf -0.017 1.0000
## L_S high - M high 0.071923 11.03 Inf 0.007 1.0000
## L_S high - M_M high 0.071282 9.45 Inf 0.008 1.0000
## L_S high - S high -0.105330 17.64 Inf -0.006 1.0000
## L_S high - S_L high 0.077238 12.29 Inf 0.006 1.0000
## L_S high - S_S high 0.083840 12.29 Inf 0.007 1.0000
## L_S high - L low -0.005596 12.13 Inf 0.000 1.0000
## L_S high - L_L low -0.094419 10.51 Inf -0.009 1.0000
## L_S high - L_S low -0.183875 11.39 Inf -0.016 1.0000
## L_S high - M low -0.023942 11.11 Inf -0.002 1.0000
## L_S high - M_M low -0.085322 9.66 Inf -0.009 1.0000
## L_S high - S low -0.248302 12.56 Inf -0.020 1.0000
## L_S high - S_L low 0.017118 11.01 Inf 0.002 1.0000
## L_S high - S_S low -0.080414 10.33 Inf -0.008 1.0000
## M high - M_M high -0.000641 9.56 Inf 0.000 1.0000
## M high - S high -0.177254 17.20 Inf -0.010 1.0000
## M high - S_L high 0.005314 12.10 Inf 0.000 1.0000
## M high - S_S high 0.011917 11.92 Inf 0.001 1.0000
## M high - L low -0.077519 12.35 Inf -0.006 1.0000
## M high - L_L low -0.166343 10.84 Inf -0.015 1.0000
## M high - L_S low -0.255798 11.64 Inf -0.022 1.0000
## M high - M low -0.095865 11.42 Inf -0.008 1.0000
## M high - M_M low -0.157245 9.96 Inf -0.016 1.0000
## M high - S low -0.320225 12.19 Inf -0.026 1.0000
## M high - S_L low -0.054805 10.91 Inf -0.005 1.0000
## M high - S_S low -0.152337 10.30 Inf -0.015 1.0000
## M_M high - S high -0.176613 16.56 Inf -0.011 1.0000
## M_M high - S_L high 0.005955 10.88 Inf 0.001 1.0000
## M_M high - S_S high 0.012558 10.81 Inf 0.001 1.0000
## M_M high - L low -0.076878 10.94 Inf -0.007 1.0000
## M_M high - L_L low -0.165702 9.09 Inf -0.018 1.0000
## M_M high - L_S low -0.255157 10.06 Inf -0.025 1.0000
## M_M high - M low -0.095225 9.72 Inf -0.010 1.0000
## M_M high - M_M low -0.156604 8.04 Inf -0.019 1.0000
## M_M high - S low -0.319584 11.16 Inf -0.029 1.0000
## M_M high - S_L low -0.054164 9.53 Inf -0.006 1.0000
## M_M high - S_S low -0.151697 8.65 Inf -0.018 1.0000
## S high - S_L high 0.182568 13.87 Inf 0.013 1.0000
## S high - S_S high 0.189170 11.58 Inf 0.016 1.0000
## S high - L low 0.099735 21.90 Inf 0.005 1.0000
## S high - L_L low 0.010911 20.76 Inf 0.001 1.0000
## S high - L_S low -0.078544 20.35 Inf -0.004 1.0000
## S high - M low 0.081388 19.44 Inf 0.004 1.0000
## S high - M_M low 0.020009 18.46 Inf 0.001 1.0000
## S high - S low -0.142971 13.67 Inf -0.010 1.0000
## S high - S_L low 0.122449 17.07 Inf 0.007 1.0000
## S high - S_S low 0.024916 13.76 Inf 0.002 1.0000
## S_L high - S_S high 0.006602 9.71 Inf 0.001 1.0000
## S_L high - L low -0.082834 15.48 Inf -0.005 1.0000
## S_L high - L_L low -0.171657 14.06 Inf -0.012 1.0000
## S_L high - L_S low -0.261113 14.20 Inf -0.018 1.0000
## S_L high - M low -0.101180 13.50 Inf -0.007 1.0000
## S_L high - M_M low -0.162560 12.21 Inf -0.013 1.0000
## S_L high - S low -0.325540 10.99 Inf -0.030 1.0000
## S_L high - S_L low -0.060120 12.01 Inf -0.005 1.0000
## S_L high - S_S low -0.157652 9.60 Inf -0.016 1.0000
## S_S high - L low -0.089436 16.16 Inf -0.006 1.0000
## S_S high - L_L low -0.178259 14.76 Inf -0.012 1.0000
## S_S high - L_S low -0.267715 14.69 Inf -0.018 1.0000
## S_S high - M low -0.107782 13.88 Inf -0.008 1.0000
## S_S high - M_M low -0.169162 12.57 Inf -0.013 1.0000
## S_S high - S low -0.332142 9.64 Inf -0.034 1.0000
## S_S high - S_L low -0.066722 11.81 Inf -0.006 1.0000
## S_S high - S_S low -0.164254 8.64 Inf -0.019 1.0000
## L low - L_L low -0.088824 9.48 Inf -0.009 1.0000
## L low - L_S low -0.178279 11.09 Inf -0.016 1.0000
## L low - M low -0.018346 11.44 Inf -0.002 1.0000
## L low - M_M low -0.079726 10.06 Inf -0.008 1.0000
## L low - S low -0.242706 15.71 Inf -0.015 1.0000
## L low - S_L low 0.022714 12.44 Inf 0.002 1.0000
## L low - S_S low -0.074818 13.45 Inf -0.006 1.0000
## L_L low - L_S low -0.089455 9.54 Inf -0.009 1.0000
## L_L low - M low 0.070477 9.82 Inf 0.007 1.0000
## L_L low - M_M low 0.009098 8.14 Inf 0.001 1.0000
## L_L low - S low -0.153882 14.35 Inf -0.011 1.0000
## L_L low - S_L low 0.111538 10.91 Inf 0.010 1.0000
## L_L low - S_S low 0.014005 11.81 Inf 0.001 1.0000
## L_S low - M low 0.159933 11.00 Inf 0.015 1.0000
## L_S low - M_M low 0.098553 9.53 Inf 0.010 1.0000
## L_S low - S low -0.064427 14.47 Inf -0.004 1.0000
## L_S low - S_L low 0.200993 11.69 Inf 0.017 1.0000
## L_S low - S_S low 0.103460 12.13 Inf 0.009 1.0000
## M low - M_M low -0.061380 9.42 Inf -0.007 1.0000
## M low - S low -0.224360 13.83 Inf -0.016 1.0000
## M low - S_L low 0.041060 11.43 Inf 0.004 1.0000
## M low - S_S low -0.056472 11.41 Inf -0.005 1.0000
## M_M low - S low -0.162980 12.56 Inf -0.013 1.0000
## M_M low - S_L low 0.102440 9.97 Inf 0.010 1.0000
## M_M low - S_S low 0.004908 9.91 Inf 0.000 1.0000
## S low - S_L low 0.265420 12.12 Inf 0.022 1.0000
## S low - S_S low 0.167887 9.84 Inf 0.017 1.0000
## S_L low - S_S low -0.097532 10.20 Inf -0.010 1.0000
##
## Results are given on the log (not the response) scale.
## P value adjustment: tukey method for comparing a family of 16 estimateshigh_L = c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_L_L = c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_L_S = c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_M = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_M_M = c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_S = c(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_S_L = c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
high_S_S = c(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
n_of_digits = 3
contrasts = contrast(emmeans_output,
method = list("high S_L - S" = high_S_L - high_S,
"high S_L - S_S" = high_S_L - high_S_S,
"high S_S - S" = high_S_S - high_S,
"high M_M - M" = high_M_M - high_M,
"high L_S - L" = high_L_S - high_L,
"high L_S - L_L" = high_L_S - high_L_L,
"high L_L - L" = high_L_L - high_L,
"low S_L - S" = low_S_L - low_S,
"low S_L - S_S" = low_S_L - low_S_S,
"low S_S - S" = low_S_S - low_S,
"low M_M - M" = low_M_M - low_M,
"low L_S - L" = low_L_S - low_L,
"low L_S - L_L" = low_L_S - low_L_L,
"low L_L - L" = low_L_L - low_L)) %>%
as.data.frame() %>%
mutate(p.value = round(p.value, digits = n_of_digits),
estimate = round(estimate, digits = n_of_digits),
SE = round(SE, digits = n_of_digits),
df = round(df, digits = n_of_digits),
z.ratio = round(z.ratio, digits = n_of_digits),
e = "",
e = ifelse(p.value > 0.1,
"",
e),
e = ifelse(p.value < 0.05,
"*",
e),
e = ifelse(p.value < 0.01,
"**",
e),
e = ifelse(p.value < 0.001,
"***",
e)) %>%
rename(" " = e)# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #
contrasts## contrast estimate SE df z.ratio p.value
## 1 high S_L - S -0.183 13.873 Inf -0.013 0.989
## 2 high S_L - S_S 0.007 9.706 Inf 0.001 0.999
## 3 high S_S - S -0.189 11.584 Inf -0.016 0.987
## 4 high M_M - M 0.001 9.562 Inf 0.000 1.000
## 5 high L_S - L 0.117 10.968 Inf 0.011 0.992
## 6 high L_S - L_L 0.075 9.564 Inf 0.008 0.994
## 7 high L_L - L 0.041 9.546 Inf 0.004 0.997
## 8 low S_L - S -0.265 12.123 Inf -0.022 0.983
## 9 low S_L - S_S -0.098 10.204 Inf -0.010 0.992
## 10 low S_S - S -0.168 9.839 Inf -0.017 0.986
## 11 low M_M - M 0.061 9.423 Inf 0.007 0.995
## 12 low L_S - L 0.178 11.095 Inf 0.016 0.987
## 13 low L_S - L_L 0.089 9.538 Inf 0.009 0.993
## 14 low L_L - L 0.089 9.479 Inf 0.009 0.993# --- CONSTRUCT RESIDUALS VS FITTED VALUES PLOT --- #
res_vs_fit = data_for_analysis %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
data_for_analysis$culture_ID,
"<br>",
"Day: ",
data_for_analysis$day,
"<br>",
"Patch Type: ",
data_for_analysis$ecosystem_type,
"<br>",
"Biomass density: ",
round(data_for_analysis$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
data_for_analysis$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))# --- PLOT RESIDUALS --- #
qqnorm(resid(full_model))
qqline(resid(full_model))
res_vs_fit\(S\) vs \(M\) vs \(L\)
ecosystem_type_selected = c("Small unconnected",
"Medium unconnected",
"Large unconnected")Shannon
response_variable_selected = "shannon"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- CALCULATE BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines,
!is.na(!!sym(response_variable_selected))) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0166906 (tol = 0.002, component 1)reduced_model = lmer(get(response_variable_selected) ~
ecosystem_size +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0240792 (tol = 0.002, component 1)null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00237388 (tol = 0.002, component 1)Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -18 < 0.001 **** very strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 53.8 86.0 -12.9 25.8 60
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.77 -0.59 -0.07 0.45 2.83
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e-02 0.28
## day 2e-04 0.01 -0.97
## Residual 7e-02 0.27
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.46 0.08 17.14 19.3 5e-13
## ecosystem_sizeMedium -0.18 0.09 12.40 -1.9 0.08
## ecosystem_sizeSmall -0.65 0.11 12.74 -5.8 7e-05
## scale(day) -0.09 0.08 18.83 -1.1 0.27
## scale(water_addition_ml) -0.01 0.07 57.38 -0.2 0.83
## scale(baseline) 0.03 0.05 11.54 0.7 0.52
## ecosystem_sizeMedium:scale(day) 0.24 0.10 16.19 2.5 0.02
## ecosystem_sizeSmall:scale(day) -0.14 0.12 15.85 -1.2 0.26
## scale(day):scale(water_addition_ml) -0.07 0.06 64.32 -1.1 0.27
## scale(day):scale(baseline) -0.06 0.05 14.21 -1.3 0.21
##
## (Intercept) ***
## ecosystem_sizeMedium .
## ecosystem_sizeSmall ***
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## ecosystem_sizeMedium:scale(day) *
## ecosystem_sizeSmall:scale(day)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) e_M:() e_S:() s():(_
## ecsystm_szM -0.668
## ecsystm_szS -0.721 0.509
## scale(day) -0.010 0.039 0.005
## scl(wtr_d_) 0.237 0.102 0.030 0.221
## scale(bsln) -0.374 0.168 0.592 -0.021 -0.024
## ecsyst_M:() 0.083 0.024 -0.012 -0.703 0.069 -0.005
## ecsyst_S:() -0.026 0.005 0.093 -0.738 -0.079 0.069 0.495
## scl(d):(__) 0.417 -0.037 -0.085 -0.026 0.811 -0.056 0.238 0.024
## scl(dy):s() -0.041 0.007 0.072 -0.372 -0.050 0.104 0.157 0.597 -0.030
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0166906 (tol = 0.002, component 1)Click to view the full model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -12.5 < 0.001 **** very strongReduced model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 59.3 86.9 -17.6 35.3 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.95 -0.66 -0.02 0.35 2.89
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.58
## day 9e-04 0.03 -1.00
## Residual 7e-02 0.27
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.449 0.073 17.525 20.0 2e-13
## ecosystem_sizeMedium -0.177 0.087 12.355 -2.0 0.06
## ecosystem_sizeSmall -0.624 0.107 13.025 -5.8 6e-05
## scale(day) -0.048 0.058 18.053 -0.8 0.42
## scale(water_addition_ml) -0.021 0.069 56.816 -0.3 0.76
## scale(baseline) 0.038 0.043 11.523 0.9 0.40
## scale(day):scale(water_addition_ml) -0.079 0.060 64.295 -1.3 0.19
## scale(day):scale(baseline) -0.003 0.054 13.857 -0.1 0.96
##
## (Intercept) ***
## ecosystem_sizeMedium .
## ecosystem_sizeSmall ***
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) s():(_
## ecsystm_szM -0.666
## ecsystm_szS -0.718 0.515
## scale(day) -0.004 0.081 0.077
## scl(wtr_d_) 0.244 0.111 0.042 0.295
## scale(bsln) -0.373 0.171 0.593 0.022 -0.020
## scl(d):(__) 0.443 -0.046 -0.092 0.118 0.806 -0.059
## scl(dy):s() -0.008 0.008 0.006 0.010 0.015 0.024 -0.004
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0240792 (tol = 0.002, component 1)Click to view the reduced model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- CALCULATE BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines,
!is.na(!!sym(response_variable_selected))) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_size +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.249836 (tol = 0.002, component 1)null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -16.8 < 0.001 **** very strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 186.6 219.1 -79.3 158.6 61
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.32 -0.43 0.02 0.55 2.27
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-01 0.489
## day 3e-05 0.005 -1.00
## Residual 4e-01 0.626
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.20 0.23 18.94 14.1 2e-11
## ecosystem_sizeMedium -1.65 0.33 15.87 -4.9 2e-04
## ecosystem_sizeSmall -2.36 0.32 15.73 -7.4 2e-06
## scale(day) -0.55 0.15 57.73 -3.8 4e-04
## scale(water_addition_ml) 0.23 0.16 62.34 1.5 0.1
## scale(baseline) 0.06 0.16 15.30 0.4 0.7
## ecosystem_sizeMedium:scale(day) -0.04 0.21 57.24 -0.2 0.8
## ecosystem_sizeSmall:scale(day) 0.09 0.19 56.48 0.5 0.6
## scale(day):scale(water_addition_ml) -0.03 0.14 65.00 -0.3 0.8
## scale(day):scale(baseline) 0.04 0.09 56.25 0.4 0.7
##
## (Intercept) ***
## ecosystem_sizeMedium ***
## ecosystem_sizeSmall ***
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## ecosystem_sizeMedium:scale(day)
## ecosystem_sizeSmall:scale(day)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) e_M:() e_S:() s():(_
## ecsystm_szM -0.645
## ecsystm_szS -0.644 0.327
## scale(day) -0.146 0.117 0.105
## scl(wtr_d_) 0.182 0.077 0.019 0.237
## scale(bsln) 0.054 -0.404 0.292 -0.006 -0.027
## ecsyst_M:() 0.168 -0.108 -0.064 -0.664 0.124 0.024
## ecsyst_S:() 0.089 -0.058 -0.108 -0.669 -0.106 -0.023 0.346
## scl(d):(__) 0.307 -0.005 -0.054 -0.059 0.817 -0.029 0.303 0.035
## scl(dy):s() -0.030 0.031 -0.022 0.050 -0.087 -0.080 -0.399 0.287 -0.090
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -20.4 < 0.001 **** very strongReduced model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 183.0 210.8 -79.5 159.0 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.27 -0.45 0.02 0.49 2.43
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-01 0.483
## day 2e-05 0.005 -1.00
## Residual 4e-01 0.628
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.202 0.223 18.333 14.3 2e-11
## ecosystem_sizeMedium -1.655 0.331 15.827 -5.0 1e-04
## ecosystem_sizeSmall -2.351 0.316 15.677 -7.4 2e-06
## scale(day) -0.534 0.086 58.725 -6.2 5e-08
## scale(water_addition_ml) 0.250 0.155 62.386 1.6 0.1
## scale(baseline) 0.068 0.155 15.423 0.4 0.7
## scale(day):scale(water_addition_ml) -0.019 0.132 64.577 -0.1 0.9
## scale(day):scale(baseline) 0.008 0.074 56.459 0.1 0.9
##
## (Intercept) ***
## ecosystem_sizeMedium ***
## ecosystem_sizeSmall ***
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) s():(_
## ecsystm_szM -0.640
## ecsystm_szS -0.643 0.322
## scale(day) -0.031 0.062 0.034
## scl(wtr_d_) 0.173 0.089 0.014 0.430
## scale(bsln) 0.051 -0.405 0.293 -0.010 -0.036
## scl(d):(__) 0.279 0.027 -0.044 0.194 0.825 -0.041
## scl(dy):s() 0.029 -0.003 -0.008 -0.006 0.044 -0.066 0.086
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.249836 (tol = 0.002, component 1)Click to view the reduced model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- CALCULATE BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines,
!is.na(!!sym(response_variable_selected))) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.202233 (tol = 0.002, component 1)reduced_model = lmer(get(response_variable_selected) ~
ecosystem_size +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0531313 (tol = 0.002, component 1)null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -16.1 < 0.001 **** very strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 285.8 318.3 -128.9 257.8 61
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.96 -0.63 -0.06 0.55 2.78
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-01 4e-01
## day 5e-07 7e-04 -0.35
## Residual 2e+00 1e+00
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.80 0.35 19.94 19.2 2e-14
## ecosystem_sizeMedium -1.68 0.45 14.98 -3.7 0.002
## ecosystem_sizeSmall -3.76 0.52 14.48 -7.2 4e-06
## scale(day) 0.21 0.31 60.49 0.7 0.507
## scale(water_addition_ml) 0.05 0.32 68.17 0.1 0.887
## scale(baseline) 0.24 0.23 13.79 1.0 0.315
## ecosystem_sizeMedium:scale(day) -0.10 0.40 60.53 -0.3 0.802
## ecosystem_sizeSmall:scale(day) -0.97 0.45 59.51 -2.2 0.034
## scale(day):scale(water_addition_ml) -0.28 0.28 70.26 -1.0 0.315
## scale(day):scale(baseline) -0.17 0.20 59.30 -0.9 0.386
##
## (Intercept) ***
## ecosystem_sizeMedium **
## ecosystem_sizeSmall ***
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## ecosystem_sizeMedium:scale(day)
## ecosystem_sizeSmall:scale(day) *
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) e_M:() e_S:() s():(_
## ecsystm_szM -0.621
## ecsystm_szS -0.681 0.386
## scale(day) -0.091 0.102 0.075
## scl(wtr_d_) 0.238 0.104 0.029 0.256
## scale(bsln) -0.228 -0.098 0.527 0.008 -0.013
## ecsyst_M:() 0.155 -0.055 -0.055 -0.657 0.100 -0.011
## ecsyst_S:() 0.042 -0.046 -0.034 -0.710 -0.113 -0.004 0.388
## scl(d):(__) 0.404 -0.019 -0.068 -0.030 0.818 -0.026 0.289 0.015
## scl(dy):s() -0.021 -0.006 -0.002 -0.224 -0.076 0.000 -0.106 0.523 -0.066
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.202233 (tol = 0.002, component 1)Click to view the full model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -15.4 < 0.001 **** very strongReduced model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 286.6 314.4 -131.3 262.6 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.83 -0.62 0.01 0.54 2.70
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-03 0.06
## day 4e-04 0.02 -0.98
## Residual 2e+00 1.35
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.78 0.35 20.42 19.3 1e-14
## ecosystem_sizeMedium -1.71 0.45 16.23 -3.8 0.002
## ecosystem_sizeSmall -3.70 0.52 15.89 -7.1 3e-06
## scale(day) -0.19 0.19 49.77 -1.0 0.316
## scale(water_addition_ml) -0.05 0.33 69.14 -0.1 0.885
## scale(baseline) 0.26 0.23 14.95 1.2 0.268
## scale(day):scale(water_addition_ml) -0.31 0.28 70.21 -1.1 0.271
## scale(day):scale(baseline) 0.09 0.16 40.82 0.6 0.565
##
## (Intercept) ***
## ecosystem_sizeMedium **
## ecosystem_sizeSmall ***
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) s():(_
## ecsystm_szM -0.627
## ecsystm_szS -0.679 0.390
## scale(day) 0.035 0.099 0.065
## scl(wtr_d_) 0.233 0.104 0.044 0.425
## scale(bsln) -0.224 -0.096 0.525 0.006 -0.003
## scl(d):(__) 0.400 -0.027 -0.057 0.201 0.829 -0.017
## scl(dy):s() 0.011 0.005 0.002 0.019 0.046 0.066 0.038
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0531313 (tol = 0.002, component 1)Click to view the reduced model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- CALCULATE BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines,
!is.na(!!sym(response_variable_selected))) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_size +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.5 0.074 * weakFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## -56.1 -24.2 42.1 -84.1 58
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2 -0.5 0.1 0.7 2.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-03 0.094
## day 4e-05 0.006 -1.00
## Residual 2e-02 0.128
## Number of obs: 72, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.773 0.036 28.845 21.3 <2e-16
## ecosystem_sizeMedium 0.026 0.045 21.545 0.6 0.56
## ecosystem_sizeSmall -0.005 0.052 22.287 -0.1 0.93
## scale(day) -0.072 0.037 27.372 -2.0 0.06
## scale(water_addition_ml) -0.034 0.034 65.834 -1.0 0.31
## scale(baseline) -0.004 0.021 20.106 -0.2 0.84
## ecosystem_sizeMedium:scale(day) 0.131 0.048 23.662 2.7 0.01
## ecosystem_sizeSmall:scale(day) 0.004 0.054 21.872 0.1 0.94
## scale(day):scale(water_addition_ml) -0.031 0.029 65.410 -1.1 0.29
## scale(day):scale(baseline) -0.009 0.022 20.037 -0.4 0.69
##
## (Intercept) ***
## ecosystem_sizeMedium
## ecosystem_sizeSmall
## scale(day) .
## scale(water_addition_ml)
## scale(baseline)
## ecosystem_sizeMedium:scale(day) *
## ecosystem_sizeSmall:scale(day)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) e_M:() e_S:() s():(_
## ecsystm_szM -0.692
## ecsystm_szS -0.708 0.564
## scale(day) 0.130 -0.069 -0.094
## scl(wtr_d_) 0.261 0.090 0.036 0.237
## scale(bsln) -0.393 0.292 0.539 -0.080 -0.052
## ecsyst_M:() -0.020 0.174 0.075 -0.726 0.068 0.046
## ecsyst_S:() -0.116 0.092 0.241 -0.737 -0.061 0.129 0.559
## scl(d):(__) 0.427 -0.039 -0.070 0.000 0.831 -0.078 0.230 0.045
## scl(dy):s() -0.084 0.056 0.125 -0.391 -0.051 0.249 0.287 0.536 -0.015
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3.9 0.93 noneReduced model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## -51.7 -24.4 37.9 -75.7 60
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8 -0.5 0.1 0.6 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-02 0.18
## day 1e-04 0.01 -1.00
## Residual 2e-02 0.13
## Number of obs: 72, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.777 0.038 28.795 20.3 <2e-16
## ecosystem_sizeMedium -0.016 0.046 29.047 -0.3 0.74
## ecosystem_sizeSmall 0.002 0.052 34.204 0.0 0.96
## scale(day) -0.026 0.025 21.017 -1.0 0.32
## scale(water_addition_ml) -0.047 0.034 62.999 -1.4 0.17
## scale(baseline) -0.003 0.023 15.912 -0.1 0.89
## scale(day):scale(water_addition_ml) -0.050 0.029 64.319 -1.7 0.09
## scale(day):scale(baseline) -0.009 0.023 15.145 -0.4 0.70
##
## (Intercept) ***
## ecosystem_sizeMedium
## ecosystem_sizeSmall
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml) .
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) s():(_
## ecsystm_szM -0.703
## ecsystm_szS -0.691 0.588
## scale(day) 0.207 0.091 0.100
## scl(wtr_d_) 0.250 0.068 0.072 0.365
## scale(bsln) -0.356 0.280 0.496 0.008 -0.035
## scl(d):(__) 0.444 -0.117 -0.076 0.194 0.837 -0.079
## scl(dy):s() -0.020 0.009 -0.006 -0.004 -0.019 0.389 -0.035
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- CALCULATE BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines,
!is.na(!!sym(response_variable_selected))) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_size +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 5.8 0.699 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 1151.4 1183.7 -561.7 1123.4 60
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.89 -0.56 -0.09 0.52 2.36
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e+04 110
## day 5e+01 7 -1.00
## Residual 2e+05 477
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3647 113 60 32.4 <2e-16
## ecosystem_sizeMedium 104 146 51 0.7 0.5
## ecosystem_sizeSmall 5 167 51 0.0 1.0
## scale(day) -67 113 34 -0.6 0.6
## scale(water_addition_ml) -4 116 72 0.0 1.0
## scale(baseline) 14 78 49 0.2 0.9
## ecosystem_sizeMedium:scale(day) 130 151 27 0.9 0.4
## ecosystem_sizeSmall:scale(day) 203 169 25 1.2 0.2
## scale(day):scale(water_addition_ml) -20 101 72 -0.2 0.8
## scale(day):scale(baseline) 54 80 24 0.7 0.5
##
## (Intercept) ***
## ecosystem_sizeMedium
## ecosystem_sizeSmall
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## ecosystem_sizeMedium:scale(day)
## ecosystem_sizeSmall:scale(day)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) e_M:() e_S:() s():(_
## ecsystm_szM -0.577
## ecsystm_szS -0.645 0.280
## scale(day) -0.109 0.114 0.089
## scl(wtr_d_) 0.266 0.129 0.022 0.247
## scale(bsln) -0.168 -0.267 0.535 0.002 -0.048
## ecsyst_M:() 0.156 -0.044 -0.059 -0.628 0.085 -0.031
## ecsyst_S:() 0.073 -0.050 -0.040 -0.675 -0.073 -0.012 0.295
## scl(d):(__) 0.464 -0.011 -0.101 -0.048 0.810 -0.067 0.256 0.071
## scl(dy):s() 0.032 -0.032 -0.024 -0.179 -0.008 0.041 -0.237 0.529 0.049
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3.4 0.758 noneReduced model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## 1149.1 1176.7 -562.5 1125.1 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8 -0.6 -0.1 0.5 2.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e+04 225
## day 2e+02 13 -1.00
## Residual 2e+05 477
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3635.3 112.6 47.3 32.3 <2e-16
## ecosystem_sizeMedium 108.8 147.1 44.3 0.7 0.5
## ecosystem_sizeSmall 7.6 168.2 44.1 0.0 1.0
## scale(day) 48.6 68.2 23.6 0.7 0.5
## scale(water_addition_ml) -0.2 115.9 72.0 0.0 1.0
## scale(baseline) 16.7 78.6 44.4 0.2 0.8
## scale(day):scale(water_addition_ml) -37.6 98.3 73.3 -0.4 0.7
## scale(day):scale(baseline) 23.1 61.7 17.7 0.4 0.7
##
## (Intercept) ***
## ecosystem_sizeMedium
## ecosystem_sizeSmall
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) s():(_
## ecsystm_szM -0.581
## ecsystm_szS -0.645 0.281
## scale(day) 0.021 0.112 0.070
## scl(wtr_d_) 0.261 0.127 0.027 0.417
## scale(bsln) -0.165 -0.268 0.533 -0.032 -0.045
## scl(d):(__) 0.449 -0.009 -0.091 0.191 0.822 -0.060
## scl(dy):s() 0.068 -0.025 -0.032 -0.017 0.097 0.073 0.149
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Auto/Hetero
response_variable_selected = "auto_hetero_ratio"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point %in% time_points_model,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- CALCULATE BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines,
!is.na(!!sym(response_variable_selected))) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_size * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_size +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE)Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 4.4 0.458 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## -47.7 -15.4 37.8 -75.7 60
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1 -0.6 -0.2 0.3 3.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.140
## day 8e-05 0.009 -1.00
## Residual 2e-02 0.134
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2e-01 4e-02 3e+01 3.9 6e-04
## ecosystem_sizeMedium 2e-02 5e-02 2e+01 0.4 0.7
## ecosystem_sizeSmall -3e-02 5e-02 2e+01 -0.7 0.5
## scale(day) 2e-04 4e-02 2e+01 0.0 1.0
## scale(water_addition_ml) 2e-02 3e-02 7e+01 0.6 0.6
## scale(baseline) -9e-03 2e-02 2e+01 -0.4 0.7
## ecosystem_sizeMedium:scale(day) 7e-02 6e-02 2e+01 1.2 0.2
## ecosystem_sizeSmall:scale(day) 6e-02 5e-02 1e+01 1.2 0.3
## scale(day):scale(water_addition_ml) 4e-04 3e-02 6e+01 0.0 1.0
## scale(day):scale(baseline) -1e-02 2e-02 1e+01 -0.4 0.7
##
## (Intercept) ***
## ecosystem_sizeMedium
## ecosystem_sizeSmall
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## ecosystem_sizeMedium:scale(day)
## ecosystem_sizeSmall:scale(day)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) e_M:() e_S:() s():(_
## ecsystm_szM -0.702
## ecsystm_szS -0.692 0.555
## scale(day) 0.253 -0.199 -0.191
## scl(wtr_d_) 0.237 0.080 0.052 0.170
## scale(bsln) -0.306 0.442 0.246 -0.145 -0.030
## ecsyst_M:() -0.140 0.328 0.161 -0.733 0.106 0.175
## ecsyst_S:() -0.198 0.174 0.353 -0.714 -0.023 0.107 0.549
## scl(d):(__) 0.380 -0.011 -0.044 -0.038 0.823 0.011 0.224 0.064
## scl(dy):s() -0.103 0.178 0.106 -0.302 0.092 0.363 0.446 0.251 0.063
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2.2 0.403 noneReduced model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_size + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
##
## AIC BIC logLik deviance df.resid
## -49.8 -22.2 36.9 -73.8 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1 -0.6 -0.2 0.3 3.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-02 0.16
## day 1e-04 0.01 -1.00
## Residual 2e-02 0.13
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.162 0.038 34.636 4.3 1e-04
## ecosystem_sizeMedium -0.002 0.050 35.437 0.0 0.97
## ecosystem_sizeSmall -0.052 0.046 37.420 -1.1 0.26
## scale(day) 0.047 0.024 17.816 1.9 0.07
## scale(water_addition_ml) 0.018 0.034 67.353 0.5 0.60
## scale(baseline) -0.014 0.022 20.347 -0.7 0.52
## scale(day):scale(water_addition_ml) -0.005 0.029 68.460 -0.2 0.85
## scale(day):scale(baseline) -0.023 0.022 12.772 -1.0 0.32
##
## (Intercept) ***
## ecosystem_sizeMedium
## ecosystem_sizeSmall
## scale(day) .
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S scl(d) sc(__) scl(b) s():(_
## ecsystm_szM -0.708
## ecsystm_szS -0.678 0.572
## scale(day) 0.188 0.070 0.084
## scl(wtr_d_) 0.247 0.046 0.072 0.363
## scale(bsln) -0.285 0.409 0.230 -0.020 -0.049
## scl(d):(__) 0.426 -0.097 -0.065 0.174 0.824 -0.030
## scl(dy):s() -0.044 0.037 0.036 0.051 0.049 0.350 -0.041
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
# --- SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small unconnected"
## [1] "Medium unconnected"
## [1] "Large unconnected"
\(S_{L}\) vs \(S\)
ecosystem_type_selected = c("Small connected to large",
"Small unconnected")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -9.3 0.001 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 51.2 73.9 -13.6 27.2 37
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1 -0.6 -0.1 0.6 2.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-05 0.004
## day 2e-05 0.005 1.00
## Residual 9e-02 0.306
## Number of obs: 49, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.378 0.085 12.855 16.3
## ecosystem_typeSmall unconnected -0.594 0.113 10.479 -5.3
## scale(day) -0.042 0.068 28.406 -0.6
## scale(water_addition_ml) 0.009 0.069 43.521 0.1
## scale(baseline) -0.032 0.054 8.735 -0.6
## ecosystem_typeSmall unconnected:scale(day) -0.128 0.102 31.487 -1.3
## scale(day):scale(water_addition_ml) -0.036 0.067 43.804 -0.5
## scale(day):scale(baseline) -0.093 0.047 27.159 -2.0
## Pr(>|t|)
## (Intercept) 6e-10 ***
## ecosystem_typeSmall unconnected 3e-04 ***
## scale(day) 0.54
## scale(water_addition_ml) 0.90
## scale(baseline) 0.57
## ecosystem_typeSmall unconnected:scale(day) 0.22
## scale(day):scale(water_addition_ml) 0.60
## scale(day):scale(baseline) 0.06 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.721
## scale(day) 0.229 -0.173
## scl(wtr_d_) 0.410 -0.315 0.386
## scale(bsln) 0.013 -0.023 -0.008 -0.028
## ecsys_Su:() -0.245 0.191 -0.682 -0.300 0.025
## scl(d):(__) 0.441 -0.223 0.265 0.681 0.004 -0.457
## scl(dy):s() -0.059 0.048 -0.002 -0.052 0.123 0.087 -0.169Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -9.8 0.001 *** strongReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 50.8 71.6 -14.4 28.8 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.15 -0.70 0.01 0.51 2.55
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.107
## day 5e-05 0.007 -0.76
## Residual 1e-01 0.311
## Number of obs: 49, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.35 0.08 11.81 16.5 2e-09
## ecosystem_typeSmall unconnected -0.57 0.11 9.85 -5.1 5e-04
## scale(day) -0.10 0.05 10.39 -1.9 0.08
## scale(water_addition_ml) -0.02 0.07 41.34 -0.2 0.82
## scale(baseline) -0.03 0.05 8.22 -0.6 0.59
## scale(day):scale(water_addition_ml) -0.07 0.06 44.17 -1.2 0.25
## scale(day):scale(baseline) -0.09 0.05 8.86 -1.8 0.11
##
## (Intercept) ***
## ecosystem_typeSmall unconnected ***
## scale(day) .
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.709
## scale(day) 0.082 -0.059
## scl(wtr_d_) 0.371 -0.282 0.255
## scale(bsln) 0.020 -0.027 0.012 -0.022
## scl(d):(__) 0.390 -0.163 -0.074 0.640 0.018
## scl(dy):s() -0.041 0.033 0.076 -0.028 0.116 -0.145Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -9.2 0.001 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 82.5 105.4 -29.2 58.5 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.35 -0.69 -0.04 0.46 2.41
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.751 0.87
## day 0.001 0.04 -1.00
## Residual 0.151 0.39
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.45 0.12 18.13 12.4
## ecosystem_typeSmall unconnected -0.73 0.16 15.08 -4.5
## scale(day) -0.61 0.13 11.86 -4.6
## scale(water_addition_ml) 0.26 0.09 39.73 2.9
## scale(baseline) 0.02 0.08 12.62 0.3
## ecosystem_typeSmall unconnected:scale(day) 0.13 0.20 12.89 0.7
## scale(day):scale(water_addition_ml) 0.02 0.09 43.90 0.2
## scale(day):scale(baseline) 0.04 0.09 10.40 0.4
## Pr(>|t|)
## (Intercept) 3e-10 ***
## ecosystem_typeSmall unconnected 4e-04 ***
## scale(day) 6e-04 ***
## scale(water_addition_ml) 0.006 **
## scale(baseline) 0.756
## ecosystem_typeSmall unconnected:scale(day) 0.513
## scale(day):scale(water_addition_ml) 0.857
## scale(day):scale(baseline) 0.705
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.750
## scale(day) -0.300 0.235
## scl(wtr_d_) 0.404 -0.326 0.271
## scale(bsln) -0.290 0.396 0.104 -0.101
## ecsys_Su:() 0.152 -0.358 -0.729 -0.220 -0.153
## scl(d):(__) 0.422 -0.208 0.190 0.642 -0.060 -0.344
## scl(dy):s() 0.082 -0.157 -0.289 -0.058 -0.473 0.393 -0.096
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -10.8 < 0.001 **** very strongReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 80.9 101.9 -29.5 58.9 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.6 0.0 0.5 2.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.777 0.88
## day 0.001 0.04 -1.00
## Residual 0.152 0.39
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.44 0.12 22.43 12.5 1e-11
## ecosystem_typeSmall unconnected -0.69 0.15 26.87 -4.6 1e-04
## scale(day) -0.54 0.09 11.71 -5.9 8e-05
## scale(water_addition_ml) 0.27 0.09 42.66 3.1 0.003
## scale(baseline) 0.03 0.08 13.84 0.4 0.678
## scale(day):scale(water_addition_ml) 0.04 0.08 49.23 0.4 0.659
## scale(day):scale(baseline) 0.01 0.09 10.01 0.1 0.897
##
## (Intercept) ***
## ecosystem_typeSmall unconnected ***
## scale(day) ***
## scale(water_addition_ml) **
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.754
## scale(day) -0.278 -0.041
## scl(wtr_d_) 0.455 -0.445 0.165
## scale(bsln) -0.274 0.369 -0.012 -0.140
## scl(d):(__) 0.512 -0.376 -0.093 0.619 -0.122
## scl(dy):s() 0.024 -0.018 -0.003 0.031 -0.452 0.045
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -11.9 < 0.001 **** very strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 181.7 204.7 -78.9 157.7 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7 -0.6 -0.2 0.5 2.7
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.250 0.50
## day 0.001 0.04 -1.00
## Residual 1.279 1.13
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.38 0.30 18.09 17.7
## ecosystem_typeSmall unconnected -2.51 0.42 14.73 -6.0
## scale(day) -0.38 0.28 18.00 -1.4
## scale(water_addition_ml) 0.39 0.26 46.10 1.5
## scale(baseline) 0.03 0.20 12.20 0.1
## ecosystem_typeSmall unconnected:scale(day) -0.32 0.44 21.03 -0.7
## scale(day):scale(water_addition_ml) 0.13 0.25 44.34 0.5
## scale(day):scale(baseline) -0.10 0.20 15.37 -0.5
## Pr(>|t|)
## (Intercept) 7e-13 ***
## ecosystem_typeSmall unconnected 3e-05 ***
## scale(day) 0.2
## scale(water_addition_ml) 0.1
## scale(baseline) 0.9
## ecosystem_typeSmall unconnected:scale(day) 0.5
## scale(day):scale(water_addition_ml) 0.6
## scale(day):scale(baseline) 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.753
## scale(day) 0.316 -0.235
## scl(wtr_d_) 0.444 -0.337 0.372
## scale(bsln) -0.269 0.405 -0.055 -0.024
## ecsys_Su:() -0.305 0.237 -0.740 -0.307 0.046
## scl(d):(__) 0.451 -0.215 0.300 0.699 0.034 -0.469
## scl(dy):s() -0.120 0.089 -0.324 -0.082 0.157 0.457 -0.194
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -13.3 < 0.001 **** very strongReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 180.3 201.3 -79.1 158.3 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.6 -0.7 -0.2 0.5 2.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.250 0.50
## day 0.001 0.04 -1.00
## Residual 1.287 1.13
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.31 0.29 19.42 18.2 1e-13
## ecosystem_typeSmall unconnected -2.43 0.41 16.39 -5.9 2e-05
## scale(day) -0.53 0.19 17.29 -2.8 0.01
## scale(water_addition_ml) 0.33 0.25 46.93 1.4 0.18
## scale(baseline) 0.04 0.20 11.95 0.2 0.86
## scale(day):scale(water_addition_ml) 0.05 0.22 47.33 0.2 0.83
## scale(day):scale(baseline) -0.03 0.18 13.84 -0.2 0.85
##
## (Intercept) ***
## ecosystem_typeSmall unconnected ***
## scale(day) *
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.735
## scale(day) 0.146 -0.091
## scl(wtr_d_) 0.382 -0.280 0.225
## scale(bsln) -0.267 0.406 -0.030 -0.009
## scl(d):(__) 0.361 -0.116 -0.079 0.661 0.064
## scl(dy):s() 0.022 -0.022 0.023 0.069 0.161 0.026
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3.6 0.838 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -33.9 -11.7 28.9 -57.9 35
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.3 -0.5 0.2 0.6 2.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-03 0.038
## day 8e-06 0.003 -1.00
## Residual 2e-02 0.129
## Number of obs: 47, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.794 0.033 20.893 23.9
## ecosystem_typeSmall unconnected 0.014 0.048 16.424 0.3
## scale(day) -0.006 0.031 24.492 -0.2
## scale(water_addition_ml) -0.053 0.030 42.197 -1.7
## scale(baseline) -0.053 0.023 14.962 -2.3
## ecosystem_typeSmall unconnected:scale(day) -0.024 0.050 24.777 -0.5
## scale(day):scale(water_addition_ml) -0.049 0.029 41.381 -1.7
## scale(day):scale(baseline) -0.037 0.023 20.514 -1.6
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall unconnected 0.77
## scale(day) 0.85
## scale(water_addition_ml) 0.09 .
## scale(baseline) 0.04 *
## ecosystem_typeSmall unconnected:scale(day) 0.64
## scale(day):scale(water_addition_ml) 0.10
## scale(day):scale(baseline) 0.12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.732
## scale(day) 0.191 -0.124
## scl(wtr_d_) 0.423 -0.272 0.366
## scale(bsln) 0.291 -0.465 -0.012 -0.075
## ecsys_Su:() -0.193 0.122 -0.724 -0.244 0.010
## scl(d):(__) 0.462 -0.180 0.260 0.699 -0.058 -0.379
## scl(dy):s() 0.009 -0.009 0.337 -0.013 0.046 -0.471 -0.011
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.9 0.711 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -35.6 -15.3 28.8 -57.6 36
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2 -0.5 0.2 0.6 2.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-03 0.044
## day 1e-05 0.003 -1.00
## Residual 2e-02 0.128
## Number of obs: 47, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.79 0.03 23.28 24.0 <2e-16
## ecosystem_typeSmall unconnected 0.02 0.05 19.09 0.4 0.71
## scale(day) -0.02 0.02 22.88 -0.8 0.45
## scale(water_addition_ml) -0.06 0.03 43.33 -1.9 0.06
## scale(baseline) -0.05 0.02 13.63 -2.3 0.04
## scale(day):scale(water_addition_ml) -0.05 0.03 45.06 -2.0 0.05
## scale(day):scale(baseline) -0.04 0.02 20.20 -2.1 0.05
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## scale(day)
## scale(water_addition_ml) .
## scale(baseline) *
## scale(day):scale(water_addition_ml) *
## scale(day):scale(baseline) .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.725
## scale(day) 0.094 -0.052
## scl(wtr_d_) 0.387 -0.241 0.281
## scale(bsln) 0.298 -0.471 -0.007 -0.077
## scl(d):(__) 0.417 -0.133 -0.020 0.678 -0.063
## scl(dy):s() -0.092 0.051 -0.006 -0.147 0.085 -0.229
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.1 0.232 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 776.3 799.0 -376.2 752.3 37
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.50 -0.54 0.04 0.49 1.98
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e+04 223
## day 3e+02 17 -1.00
## Residual 3e+05 505
## Number of obs: 49, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3917 132 22 29.8
## ecosystem_typeSmall unconnected -301 174 18 -1.7
## scale(day) 134 119 16 1.1
## scale(water_addition_ml) -19 116 45 -0.2
## scale(baseline) 4 83 15 0.1
## ecosystem_typeSmall unconnected:scale(day) -3 177 19 0.0
## scale(day):scale(water_addition_ml) -85 110 43 -0.8
## scale(day):scale(baseline) 19 82 14 0.2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall unconnected 0.1
## scale(day) 0.3
## scale(water_addition_ml) 0.9
## scale(baseline) 1.0
## ecosystem_typeSmall unconnected:scale(day) 1.0
## scale(day):scale(water_addition_ml) 0.4
## scale(day):scale(baseline) 0.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.735
## scale(day) 0.286 -0.221
## scl(wtr_d_) 0.457 -0.364 0.379
## scale(bsln) -0.199 0.226 -0.083 -0.165
## ecsys_Su:() -0.282 0.245 -0.694 -0.293 0.070
## scl(d):(__) 0.487 -0.267 0.261 0.691 -0.163 -0.429
## scl(dy):s() -0.052 0.037 -0.158 -0.103 0.186 0.149 -0.029
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.9 0.087 * weakReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 774.3 795.1 -376.2 752.3 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.50 -0.54 0.04 0.49 1.98
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e+04 222
## day 3e+02 17 -1.00
## Residual 3e+05 505
## Number of obs: 49, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3916 126 25 31.0 <2e-16
## ecosystem_typeSmall unconnected -300 169 21 -1.8 0.09
## scale(day) 133 86 17 1.5 0.14
## scale(water_addition_ml) -20 111 47 -0.2 0.86
## scale(baseline) 4 83 15 0.1 0.96
## scale(day):scale(water_addition_ml) -86 99 47 -0.9 0.39
## scale(day):scale(baseline) 19 81 14 0.2 0.82
##
## (Intercept) ***
## ecosystem_typeSmall unconnected .
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.716
## scale(day) 0.130 -0.073
## scl(wtr_d_) 0.408 -0.315 0.255
## scale(bsln) -0.187 0.216 -0.049 -0.152
## scl(d):(__) 0.422 -0.185 -0.056 0.654 -0.148
## scl(dy):s() -0.011 0.000 -0.077 -0.063 0.177 0.039
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small connected to large"
## [1] "Small unconnected"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
\(S_{L}\) vs \(S_{S}\)
ecosystem_type_selected = c("Small connected to large",
"Small connected to small")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -18.3 < 0.001 **** very strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 68.4 96.0 -22.2 44.4 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.82 -0.45 0.01 0.45 2.00
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-12 1e-06
## day 5e-15 7e-08 -1.00
## Residual 1e-01 3e-01
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 1.39 0.07 74.00
## ecosystem_typeSmall connected to small -0.57 0.09 74.00
## scale(day) -0.04 0.07 74.00
## scale(water_addition_ml) -0.05 0.05 74.00
## scale(baseline) 0.05 0.04 74.00
## ecosystem_typeSmall connected to small:scale(day) -0.21 0.09 74.00
## scale(day):scale(water_addition_ml) -0.05 0.05 74.00
## scale(day):scale(baseline) 0.02 0.04 74.00
## t value Pr(>|t|)
## (Intercept) 19.4 <2e-16 ***
## ecosystem_typeSmall connected to small -6.5 9e-09 ***
## scale(day) -0.6 0.57
## scale(water_addition_ml) -1.0 0.34
## scale(baseline) 1.1 0.28
## ecosystem_typeSmall connected to small:scale(day) -2.3 0.02 *
## scale(day):scale(water_addition_ml) -1.0 0.30
## scale(day):scale(baseline) 0.4 0.70
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts scl(d) sc(__) scl(b) e_Scts: s():(_
## ecsyst_Scts -0.783
## scale(day) 0.003 -0.009
## scl(wtr_d_) 0.165 -0.032 0.166
## scale(bsln) 0.298 -0.419 0.013 0.018
## ecs_Scts:() 0.007 -0.020 -0.792 0.103 0.019
## scl(d):(__) 0.240 0.110 -0.004 0.421 -0.136 -0.039
## scl(dy):s() 0.000 0.023 0.301 -0.114 -0.030 -0.419 0.060
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -15.2 < 0.001 **** very strongReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 71.5 96.8 -24.7 49.5 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.67 -0.52 0.05 0.65 1.85
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 7e-10 3e-05
## day 3e-12 2e-06 -1.00
## Residual 1e-01 3e-01
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.39 0.07 74.00 18.8
## ecosystem_typeSmall connected to small -0.58 0.09 74.00 -6.3
## scale(day) -0.17 0.05 74.00 -3.8
## scale(water_addition_ml) -0.03 0.05 74.00 -0.7
## scale(baseline) 0.05 0.04 74.00 1.1
## scale(day):scale(water_addition_ml) -0.06 0.05 74.00 -1.1
## scale(day):scale(baseline) -0.02 0.04 74.00 -0.6
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 2e-08 ***
## scale(day) 3e-04 ***
## scale(water_addition_ml) 0.5
## scale(baseline) 0.3
## scale(day):scale(water_addition_ml) 0.3
## scale(day):scale(baseline) 0.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts scl(d) sc(__) scl(b) s():(_
## ecsyst_Scts -0.783
## scale(day) 0.015 -0.041
## scl(wtr_d_) 0.165 -0.030 0.408
## scale(bsln) 0.298 -0.419 0.046 0.016
## scl(d):(__) 0.240 0.109 -0.057 0.428 -0.136
## scl(dy):s() 0.004 0.016 -0.056 -0.079 -0.024 0.048
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -7.6 0.003 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 104.3 132.0 -40.2 80.3 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.83 -0.51 0.03 0.37 2.79
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.59
## day 5e-04 0.02 -1.00
## Residual 1e-01 0.38
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 1.26 0.11 21.34
## ecosystem_typeSmall connected to small -0.52 0.14 19.11
## scale(day) -0.60 0.11 21.37
## scale(water_addition_ml) 0.04 0.06 61.41
## scale(baseline) -0.09 0.07 19.13
## ecosystem_typeSmall connected to small:scale(day) 0.05 0.14 20.04
## scale(day):scale(water_addition_ml) -0.22 0.06 67.18
## scale(day):scale(baseline) 0.05 0.07 20.48
## t value Pr(>|t|)
## (Intercept) 11.2 2e-10 ***
## ecosystem_typeSmall connected to small -3.8 0.001 **
## scale(day) -5.5 2e-05 ***
## scale(water_addition_ml) 0.8 0.448
## scale(baseline) -1.4 0.177
## ecosystem_typeSmall connected to small:scale(day) 0.4 0.696
## scale(day):scale(water_addition_ml) -3.4 0.001 **
## scale(day):scale(baseline) 0.8 0.450
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts scl(d) sc(__) scl(b) e_Scts: s():(_
## ecsyst_Scts -0.819
## scale(day) -0.344 0.303
## scl(wtr_d_) 0.134 -0.042 0.207
## scale(bsln) 0.424 -0.490 -0.149 0.042
## ecs_Scts:() 0.289 -0.373 -0.824 -0.009 0.174
## scl(d):(__) 0.260 0.009 0.020 0.376 0.077 -0.081
## scl(dy):s() -0.114 0.177 0.421 0.109 -0.360 -0.493 0.131
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -9.5 0.001 *** strongReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 102.5 127.8 -40.2 80.5 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.85 -0.50 0.04 0.37 2.84
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-01 0.60
## day 5e-04 0.02 -1.00
## Residual 1e-01 0.38
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.24 0.11 30.31 11.5
## ecosystem_typeSmall connected to small -0.50 0.13 30.22 -3.9
## scale(day) -0.56 0.06 26.35 -9.0
## scale(water_addition_ml) 0.05 0.06 61.33 0.8
## scale(baseline) -0.10 0.07 21.57 -1.5
## scale(day):scale(water_addition_ml) -0.21 0.06 67.17 -3.3
## scale(day):scale(baseline) 0.06 0.06 20.19 1.1
## Pr(>|t|)
## (Intercept) 1e-12 ***
## ecosystem_typeSmall connected to small 5e-04 ***
## scale(day) 2e-09 ***
## scale(water_addition_ml) 0.445
## scale(baseline) 0.150
## scale(day):scale(water_addition_ml) 0.001 **
## scale(day):scale(baseline) 0.282
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts scl(d) sc(__) scl(b) s():(_
## ecsyst_Scts -0.800
## scale(day) -0.197 -0.009
## scl(wtr_d_) 0.143 -0.048 0.353
## scale(bsln) 0.396 -0.465 -0.009 0.044
## scl(d):(__) 0.297 -0.024 -0.084 0.376 0.094
## scl(dy):s() 0.034 -0.008 0.029 0.120 -0.322 0.105
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -25.2 < 0.001 **** very strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 238.9 266.6 -107.5 214.9 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.63 -0.65 -0.06 0.44 3.07
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 2e-15 4e-08 NaN
## Residual 1e+00 1e+00
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 5.19 0.22 74.00
## ecosystem_typeSmall connected to small -2.06 0.26 74.00
## scale(day) -0.53 0.22 74.00
## scale(water_addition_ml) 0.01 0.15 74.00
## scale(baseline) 0.22 0.12 74.00
## ecosystem_typeSmall connected to small:scale(day) -0.33 0.26 74.00
## scale(day):scale(water_addition_ml) -0.20 0.16 74.00
## scale(day):scale(baseline) -0.02 0.12 74.00
## t value Pr(>|t|)
## (Intercept) 23.9 <2e-16 ***
## ecosystem_typeSmall connected to small -8.1 1e-11 ***
## scale(day) -2.5 0.02 *
## scale(water_addition_ml) 0.1 0.94
## scale(baseline) 1.8 0.07 .
## ecosystem_typeSmall connected to small:scale(day) -1.3 0.20
## scale(day):scale(water_addition_ml) -1.3 0.21
## scale(day):scale(baseline) -0.2 0.87
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts scl(d) sc(__) scl(b) e_Scts: s():(_
## ecsyst_Scts -0.759
## scale(day) -0.004 -0.008
## scl(wtr_d_) 0.171 -0.025 0.208
## scale(bsln) 0.022 -0.055 0.008 -0.003
## ecs_Scts:() 0.008 -0.010 -0.769 0.066 0.001
## scl(d):(__) 0.295 0.062 -0.022 0.440 -0.062 -0.011
## scl(dy):s() -0.024 -0.002 0.025 -0.090 -0.006 -0.053 -0.068
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -25.5 < 0.001 **** very strongReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 238.6 263.9 -108.3 216.6 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.55 -0.68 -0.08 0.58 3.05
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-14 1e-07
## day 2e-17 5e-09 -1.00
## Residual 1e+00 1e+00
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.19 0.22 74.00 23.7
## ecosystem_typeSmall connected to small -2.06 0.26 74.00 -8.0
## scale(day) -0.74 0.14 74.00 -5.3
## scale(water_addition_ml) 0.03 0.16 74.00 0.2
## scale(baseline) 0.22 0.12 74.00 1.8
## scale(day):scale(water_addition_ml) -0.20 0.16 74.00 -1.3
## scale(day):scale(baseline) -0.03 0.12 74.00 -0.2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 1e-11 ***
## scale(day) 1e-06 ***
## scale(water_addition_ml) 0.87
## scale(baseline) 0.08 .
## scale(day):scale(water_addition_ml) 0.21
## scale(day):scale(baseline) 0.81
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts scl(d) sc(__) scl(b) s():(_
## ecsyst_Scts -0.759
## scale(day) 0.003 -0.024
## scl(wtr_d_) 0.171 -0.025 0.405
## scale(bsln) 0.022 -0.055 0.013 -0.003
## scl(d):(__) 0.295 0.061 -0.048 0.442 -0.062
## scl(dy):s() -0.023 -0.002 -0.025 -0.087 -0.006 -0.069
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2.8 0.537 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -80.9 -54.3 52.5 -104.9 56
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7 -0.6 0.3 0.6 2.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-16 1e-08
## day 3e-19 5e-10 -1.00
## Residual 1e-02 1e-01
## Number of obs: 68, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 8e-01 3e-02 7e+01
## ecosystem_typeSmall connected to small -5e-03 3e-02 7e+01
## scale(day) 3e-02 3e-02 7e+01
## scale(water_addition_ml) -3e-02 2e-02 7e+01
## scale(baseline) -2e-02 2e-02 7e+01
## ecosystem_typeSmall connected to small:scale(day) -4e-02 3e-02 7e+01
## scale(day):scale(water_addition_ml) -7e-04 2e-02 7e+01
## scale(day):scale(baseline) 2e-02 2e-02 7e+01
## t value Pr(>|t|)
## (Intercept) 32.7 <2e-16 ***
## ecosystem_typeSmall connected to small -0.2 0.88
## scale(day) 1.2 0.25
## scale(water_addition_ml) -2.0 0.05 *
## scale(baseline) -1.2 0.22
## ecosystem_typeSmall connected to small:scale(day) -1.1 0.27
## scale(day):scale(water_addition_ml) 0.0 0.97
## scale(day):scale(baseline) 1.1 0.29
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts scl(d) sc(__) scl(b) e_Scts: s():(_
## ecsyst_Scts -0.781
## scale(day) -0.023 0.026
## scl(wtr_d_) 0.160 -0.041 0.200
## scale(bsln) 0.380 -0.505 0.006 0.041
## ecs_Scts:() 0.020 -0.034 -0.782 0.087 0.017
## scl(d):(__) 0.250 0.096 0.057 0.375 -0.091 -0.103
## scl(dy):s() 0.031 0.023 0.375 -0.045 -0.037 -0.510 0.175
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2 0.848 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -81.7 -57.3 51.9 -103.7 57
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.6 0.3 0.6 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e-10 3e-05
## day 2e-12 1e-06 -1.00
## Residual 1e-02 1e-01
## Number of obs: 68, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.834 0.026 68.000 32.4
## ecosystem_typeSmall connected to small -0.006 0.033 68.000 -0.2
## scale(day) 0.008 0.016 68.000 0.5
## scale(water_addition_ml) -0.033 0.017 68.000 -1.9
## scale(baseline) -0.019 0.016 68.000 -1.2
## scale(day):scale(water_addition_ml) -0.003 0.018 68.000 -0.2
## scale(day):scale(baseline) 0.008 0.014 68.000 0.6
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 0.85
## scale(day) 0.63
## scale(water_addition_ml) 0.06 .
## scale(baseline) 0.23
## scale(day):scale(water_addition_ml) 0.88
## scale(day):scale(baseline) 0.56
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts scl(d) sc(__) scl(b) s():(_
## ecsyst_Scts -0.781
## scale(day) -0.012 -0.001
## scl(wtr_d_) 0.158 -0.039 0.432
## scale(bsln) 0.380 -0.505 0.030 0.039
## scl(d):(__) 0.253 0.093 -0.038 0.387 -0.090
## scl(dy):s() 0.047 0.007 -0.045 -0.001 -0.033 0.143
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2.6 0.492 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1173.1 1200.7 -574.5 1149.1 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9 -0.7 0.1 0.7 2.1
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e+05 391
## day 5e+02 23 -1.00
## Residual 3e+05 552
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 3923 120 40
## ecosystem_typeSmall connected to small -149 142 36
## scale(day) 191 129 19
## scale(water_addition_ml) 62 84 67
## scale(baseline) -43 68 37
## ecosystem_typeSmall connected to small:scale(day) 70 155 18
## scale(day):scale(water_addition_ml) -104 89 70
## scale(day):scale(baseline) -128 74 19
## t value Pr(>|t|)
## (Intercept) 32.6 <2e-16 ***
## ecosystem_typeSmall connected to small -1.1 0.3
## scale(day) 1.5 0.2
## scale(water_addition_ml) 0.7 0.5
## scale(baseline) -0.6 0.5
## ecosystem_typeSmall connected to small:scale(day) 0.4 0.7
## scale(day):scale(water_addition_ml) -1.2 0.2
## scale(day):scale(baseline) -1.7 0.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts scl(d) sc(__) scl(b) e_Scts: s():(_
## ecsyst_Scts -0.758
## scale(day) 0.115 -0.107
## scl(wtr_d_) 0.180 -0.024 0.189
## scale(bsln) -0.036 0.008 -0.025 -0.144
## ecs_Scts:() -0.093 0.116 -0.778 0.053 -0.012
## scl(d):(__) 0.302 0.057 -0.014 0.466 -0.086 -0.015
## scl(dy):s() -0.053 -0.014 -0.007 -0.097 0.145 0.015 -0.172
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.8 0.27 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1171.3 1196.6 -574.6 1149.3 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8 -0.7 0.1 0.7 2.1
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e+05 402
## day 6e+02 24 -1.00
## Residual 3e+05 553
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3928 120 44 32.7
## ecosystem_typeSmall connected to small -156 140 43 -1.1
## scale(day) 236 82 25 2.9
## scale(water_addition_ml) 60 84 67 0.7
## scale(baseline) -43 68 37 -0.6
## scale(day):scale(water_addition_ml) -103 89 70 -1.2
## scale(day):scale(baseline) -129 75 19 -1.7
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 0.273
## scale(day) 0.008 **
## scale(water_addition_ml) 0.482
## scale(baseline) 0.531
## scale(day):scale(water_addition_ml) 0.252
## scale(day):scale(baseline) 0.102
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts scl(d) sc(__) scl(b) s():(_
## ecsyst_Scts -0.755
## scale(day) 0.069 -0.026
## scl(wtr_d_) 0.186 -0.030 0.364
## scale(bsln) -0.037 0.010 -0.055 -0.143
## scl(d):(__) 0.302 0.059 -0.041 0.467 -0.086
## scl(dy):s() -0.052 -0.016 0.007 -0.098 0.147 -0.171
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small connected to large"
## [1] "Small connected to small"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
\(S_{S}\) vs \(S\)
ecosystem_type_selected = c("Small connected to small",
"Small unconnected")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3 0.618 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 90.7 118.2 -33.4 66.7 61
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.78 -0.50 0.06 0.66 2.15
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.12
## day 1e-04 0.01 -1.00
## Residual 1e-01 0.37
## Number of obs: 73, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.81 0.07 29.05 11.8
## ecosystem_typeSmall unconnected -0.04 0.11 21.49 -0.4
## scale(day) -0.23 0.06 36.57 -3.6
## scale(water_addition_ml) -0.02 0.06 70.04 -0.4
## scale(baseline) -0.01 0.05 18.77 -0.3
## ecosystem_typeSmall unconnected:scale(day) 0.09 0.12 34.32 0.8
## scale(day):scale(water_addition_ml) -0.11 0.06 66.90 -1.8
## scale(day):scale(baseline) -0.01 0.05 29.11 -0.3
## Pr(>|t|)
## (Intercept) 1e-12 ***
## ecosystem_typeSmall unconnected 0.72
## scale(day) 9e-04 ***
## scale(water_addition_ml) 0.71
## scale(baseline) 0.80
## ecosystem_typeSmall unconnected:scale(day) 0.42
## scale(day):scale(water_addition_ml) 0.07 .
## scale(day):scale(baseline) 0.79
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.610
## scale(day) 0.199 -0.155
## scl(wtr_d_) 0.300 -0.210 0.407
## scale(bsln) -0.209 0.376 -0.012 0.040
## ecsys_Su:() -0.228 0.217 -0.575 -0.201 0.071
## scl(d):(__) 0.474 -0.170 0.138 0.486 -0.010 -0.332
## scl(dy):s() -0.027 0.075 -0.223 -0.010 0.131 0.383 0.007
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.7 0.573 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 89.4 114.6 -33.7 67.4 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.71 -0.51 0.08 0.64 2.06
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.14
## day 1e-04 0.01 -1.00
## Residual 1e-01 0.37
## Number of obs: 73, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.82 0.07 31.64 12.2 2e-13
## ecosystem_typeSmall unconnected -0.06 0.11 26.05 -0.6 0.6
## scale(day) -0.20 0.05 35.14 -3.8 6e-04
## scale(water_addition_ml) -0.01 0.06 70.77 -0.2 0.8
## scale(baseline) -0.02 0.05 19.20 -0.3 0.8
## scale(day):scale(water_addition_ml) -0.09 0.06 65.88 -1.6 0.1
## scale(day):scale(baseline) -0.03 0.05 26.81 -0.6 0.5
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.587
## scale(day) 0.099 -0.038
## scl(wtr_d_) 0.265 -0.170 0.360
## scale(bsln) -0.197 0.370 0.036 0.057
## scl(d):(__) 0.429 -0.100 -0.067 0.457 0.017
## scl(dy):s() 0.067 -0.008 -0.004 0.075 0.132 0.153
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.7 0.189 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 110.3 138.0 -43.2 86.3 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.90 -0.63 -0.04 0.48 2.98
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-02 0.29
## day 1e-04 0.01 -1.00
## Residual 2e-01 0.43
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.77 0.08 47.78 10
## ecosystem_typeSmall unconnected -0.17 0.14 37.96 -1
## scale(day) -0.58 0.08 34.76 -8
## scale(water_addition_ml) 0.08 0.07 62.15 1
## scale(baseline) -0.10 0.07 36.31 -2
## ecosystem_typeSmall unconnected:scale(day) 0.23 0.14 29.72 2
## scale(day):scale(water_addition_ml) -0.20 0.07 72.81 -3
## scale(day):scale(baseline) 0.07 0.07 30.54 1
## Pr(>|t|)
## (Intercept) 5e-13 ***
## ecosystem_typeSmall unconnected 0.243
## scale(day) 6e-09 ***
## scale(water_addition_ml) 0.237
## scale(baseline) 0.129
## ecosystem_typeSmall unconnected:scale(day) 0.121
## scale(day):scale(water_addition_ml) 0.006 **
## scale(day):scale(baseline) 0.320
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.647
## scale(day) -0.023 -0.003
## scl(wtr_d_) 0.300 -0.181 0.332
## scale(bsln) -0.327 0.587 0.047 0.066
## ecsys_Su:() -0.032 -0.069 -0.630 -0.109 -0.070
## scl(d):(__) 0.461 -0.115 0.038 0.486 0.068 -0.172
## scl(dy):s() 0.139 -0.087 -0.347 0.146 -0.081 0.544 0.230
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.1 0.342 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 110.8 136.1 -44.4 88.8 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.07 -0.55 -0.03 0.47 2.53
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-01 0.38
## day 2e-04 0.02 -1.00
## Residual 2e-01 0.43
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.773 0.080 46.659 9.6 1e-12
## ecosystem_typeSmall unconnected -0.144 0.142 44.153 -1.0 0.32
## scale(day) -0.504 0.061 29.000 -8.2 5e-09
## scale(water_addition_ml) 0.092 0.067 61.941 1.4 0.17
## scale(baseline) -0.093 0.067 39.258 -1.4 0.17
## scale(day):scale(water_addition_ml) -0.181 0.071 72.541 -2.6 0.01
## scale(day):scale(baseline) 0.009 0.061 26.975 0.2 0.88
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml) *
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.651
## scale(day) -0.082 -0.058
## scl(wtr_d_) 0.297 -0.193 0.331
## scale(bsln) -0.329 0.584 0.004 0.056
## scl(d):(__) 0.466 -0.133 -0.096 0.471 0.053
## scl(dy):s() 0.182 -0.060 -0.008 0.238 -0.082 0.382
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2.8 0.538 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 262.6 290.2 -119.3 238.6 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.54 -0.60 -0.05 0.50 2.78
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-03 0.07
## day 4e-04 0.02 -1.00
## Residual 1e+00 1.17
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3.11 0.23 23.39 13.5
## ecosystem_typeSmall unconnected -0.36 0.41 16.94 -0.9
## scale(day) -0.82 0.20 49.33 -4.1
## scale(water_addition_ml) 0.03 0.18 68.70 0.2
## scale(baseline) -0.06 0.19 16.11 -0.3
## ecosystem_typeSmall unconnected:scale(day) 0.22 0.38 47.24 0.6
## scale(day):scale(water_addition_ml) -0.33 0.19 66.24 -1.7
## scale(day):scale(baseline) -0.14 0.17 43.97 -0.8
## Pr(>|t|)
## (Intercept) 2e-12 ***
## ecosystem_typeSmall unconnected 0.40
## scale(day) 2e-04 ***
## scale(water_addition_ml) 0.87
## scale(baseline) 0.75
## ecosystem_typeSmall unconnected:scale(day) 0.56
## scale(day):scale(water_addition_ml) 0.09 .
## scale(day):scale(baseline) 0.41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.635
## scale(day) 0.187 -0.130
## scl(wtr_d_) 0.281 -0.171 0.398
## scale(bsln) -0.291 0.536 -0.010 0.068
## ecsys_Su:() -0.208 0.130 -0.623 -0.194 0.021
## scl(d):(__) 0.420 -0.102 0.162 0.497 0.083 -0.352
## scl(dy):s() -0.057 0.052 -0.320 0.021 0.091 0.543 -0.067
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.1 0.343 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 260.9 286.2 -119.4 238.9 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.47 -0.59 -0.09 0.55 2.73
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.10
## day 4e-04 0.02 -1.00
## Residual 1e+00 1.18
## Number of obs: 74, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.14 0.23 24.56 13.9 4e-13
## ecosystem_typeSmall unconnected -0.39 0.41 18.42 -1.0 0.3
## scale(day) -0.75 0.16 50.74 -4.7 2e-05
## scale(water_addition_ml) 0.05 0.18 68.82 0.3 0.8
## scale(baseline) -0.07 0.19 16.54 -0.3 0.7
## scale(day):scale(water_addition_ml) -0.29 0.18 65.18 -1.6 0.1
## scale(day):scale(baseline) -0.20 0.14 42.55 -1.4 0.2
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.626
## scale(day) 0.077 -0.063
## scl(wtr_d_) 0.252 -0.151 0.361
## scale(bsln) -0.292 0.538 0.004 0.075
## scl(d):(__) 0.381 -0.060 -0.078 0.468 0.098
## scl(dy):s() 0.068 -0.022 0.028 0.153 0.098 0.158
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.9 0.352 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -37.4 -11.3 30.7 -61.4 53
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4 -0.6 0.2 0.7 1.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 7e-04 0.027
## day 3e-06 0.002 -1.00
## Residual 2e-02 0.150
## Number of obs: 65, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.807 0.027 57.952 29.8
## ecosystem_typeSmall unconnected -0.030 0.042 52.301 -0.7
## scale(day) 0.005 0.026 36.971 0.2
## scale(water_addition_ml) -0.028 0.024 63.221 -1.1
## scale(baseline) -0.029 0.019 53.611 -1.5
## ecosystem_typeSmall unconnected:scale(day) -0.060 0.043 30.680 -1.4
## scale(day):scale(water_addition_ml) -0.027 0.025 64.583 -1.1
## scale(day):scale(baseline) 0.001 0.019 28.685 0.1
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall unconnected 0.5
## scale(day) 0.8
## scale(water_addition_ml) 0.3
## scale(baseline) 0.1
## ecosystem_typeSmall unconnected:scale(day) 0.2
## scale(day):scale(water_addition_ml) 0.3
## scale(day):scale(baseline) 0.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.587
## scale(day) 0.137 -0.120
## scl(wtr_d_) 0.313 -0.247 0.445
## scale(bsln) -0.108 0.187 -0.004 0.013
## ecsys_Su:() -0.186 0.081 -0.576 -0.196 0.018
## scl(d):(__) 0.502 -0.152 0.154 0.432 -0.026 -0.336
## scl(dy):s() 0.042 0.002 -0.115 0.011 -0.036 0.142 0.113
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.7 0.611 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -37.6 -13.6 29.8 -59.6 54
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5 -0.5 0.2 0.5 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-03 0.061
## day 2e-05 0.004 -1.00
## Residual 2e-02 0.151
## Number of obs: 65, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.800 0.027 55.424 29.6 <2e-16
## ecosystem_typeSmall unconnected -0.022 0.042 49.745 -0.5 0.6
## scale(day) -0.016 0.022 29.952 -0.7 0.5
## scale(water_addition_ml) -0.034 0.024 63.308 -1.4 0.2
## scale(baseline) -0.028 0.020 42.881 -1.4 0.2
## scale(day):scale(water_addition_ml) -0.038 0.024 62.021 -1.6 0.1
## scale(day):scale(baseline) 0.006 0.020 23.247 0.3 0.8
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.577
## scale(day) 0.070 -0.083
## scl(wtr_d_) 0.287 -0.224 0.405
## scale(bsln) -0.104 0.184 0.009 0.018
## scl(d):(__) 0.467 -0.117 -0.049 0.406 -0.018
## scl(dy):s() 0.068 -0.009 -0.039 0.041 0.014 0.169
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2.1 0.378 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1173.7 1201.2 -574.9 1149.7 61
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.7 0.1 0.6 2.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+05 542
## day 1e+03 31 -1.00
## Residual 4e+05 612
## Number of obs: 73, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3800 108 47 35.3
## ecosystem_typeSmall unconnected -235 166 37 -1.4
## scale(day) 268 113 20 2.4
## scale(water_addition_ml) 105 98 66 1.1
## scale(baseline) -110 77 35 -1.4
## ecosystem_typeSmall unconnected:scale(day) -96 198 19 -0.5
## scale(day):scale(water_addition_ml) -97 103 70 -0.9
## scale(day):scale(baseline) -102 88 17 -1.2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall unconnected 0.17
## scale(day) 0.03 *
## scale(water_addition_ml) 0.28
## scale(baseline) 0.16
## ecosystem_typeSmall unconnected:scale(day) 0.63
## scale(day):scale(water_addition_ml) 0.35
## scale(day):scale(baseline) 0.26
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) e_Su:( s():(_
## ecsystm_tSu -0.591
## scale(day) 0.216 -0.171
## scl(wtr_d_) 0.350 -0.280 0.389
## scale(bsln) -0.102 0.155 -0.094 -0.188
## ecsys_Su:() -0.251 0.216 -0.548 -0.205 0.026
## scl(d):(__) 0.525 -0.199 0.141 0.487 -0.052 -0.360
## scl(dy):s() -0.129 0.041 -0.072 -0.091 0.149 0.160 -0.215
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.3 0.191 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1172.0 1197.2 -575.0 1150.0 62
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3 -0.7 0.1 0.6 2.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+05 542
## day 1e+03 31 -1.00
## Residual 4e+05 613
## Number of obs: 73, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3787 104 55 36 <2e-16
## ecosystem_typeSmall unconnected -217 163 48 -1 0.19
## scale(day) 238 94 20 2 0.02
## scale(water_addition_ml) 96 96 69 1 0.32
## scale(baseline) -108 77 35 -1 0.17
## scale(day):scale(water_addition_ml) -115 96 68 -1 0.24
## scale(day):scale(baseline) -96 87 16 -1 0.29
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## scale(day) *
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su scl(d) sc(__) scl(b) s():(_
## ecsystm_tSu -0.568
## scale(day) 0.096 -0.065
## scl(wtr_d_) 0.315 -0.246 0.338
## scale(bsln) -0.099 0.153 -0.096 -0.186
## scl(d):(__) 0.481 -0.133 -0.072 0.453 -0.046
## scl(dy):s() -0.093 0.007 0.020 -0.061 0.146 -0.171
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small connected to small"
## [1] "Small unconnected"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
\(L_{S}\) vs \(L\)
ecosystem_type_selected = c("Large connected to small",
"Large unconnected")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -3.3 0.026 ** moderateFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 22.5 45.4 0.8 -1.5 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1 -0.5 -0.1 0.6 2.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-01 0.37
## day 2e-04 0.02 -1.00
## Residual 5e-02 0.22
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.39 0.06 25.43 22.0
## ecosystem_typeLarge unconnected 0.10 0.08 17.34 1.2
## scale(day) 0.13 0.07 12.41 2.0
## scale(water_addition_ml) -0.04 0.07 39.92 -0.6
## scale(baseline) 0.02 0.04 15.29 0.5
## ecosystem_typeLarge unconnected:scale(day) -0.32 0.10 12.51 -3.3
## scale(day):scale(water_addition_ml) -0.05 0.06 43.23 -0.8
## scale(day):scale(baseline) 0.08 0.05 10.30 1.7
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge unconnected 0.261
## scale(day) 0.068 .
## scale(water_addition_ml) 0.560
## scale(baseline) 0.604
## ecosystem_typeLarge unconnected:scale(day) 0.006 **
## scale(day):scale(water_addition_ml) 0.439
## scale(day):scale(baseline) 0.121
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.642
## scale(day) -0.105 0.179
## scl(wtr_d_) 0.514 -0.178 0.319
## scale(bsln) 0.184 -0.355 -0.103 -0.046
## ecsys_Lu:() 0.121 -0.384 -0.678 -0.050 0.148
## scl(d):(__) 0.498 0.013 0.275 0.789 -0.091 -0.252
## scl(dy):s() -0.076 0.145 0.243 -0.027 -0.347 -0.366 0.035
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.9 0.737 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 27.6 48.7 -2.8 5.6 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7 -0.6 -0.1 0.6 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-01 0.67
## day 8e-04 0.03 -1.00
## Residual 5e-02 0.22
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.43 0.07 23.08 21.4 <2e-16
## ecosystem_typeLarge unconnected -0.03 0.08 30.98 -0.4 0.7
## scale(day) -0.02 0.07 12.99 -0.3 0.8
## scale(water_addition_ml) -0.06 0.07 39.37 -0.8 0.4
## scale(baseline) 0.05 0.04 9.82 1.0 0.3
## scale(day):scale(water_addition_ml) -0.10 0.06 42.34 -1.6 0.1
## scale(day):scale(baseline) 0.02 0.06 10.15 0.4 0.7
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.618
## scale(day) -0.241 -0.084
## scl(wtr_d_) 0.506 -0.220 0.281
## scale(bsln) 0.141 -0.288 -0.003 -0.034
## scl(d):(__) 0.547 -0.111 0.089 0.790 -0.044
## scl(dy):s() -0.025 0.004 -0.003 -0.034 -0.540 -0.045
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.8 0.092 * weakFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 133.1 156.0 -54.5 109.1 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8 -0.6 -0.1 0.5 1.7
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1.235 1.11
## day 0.002 0.04 -0.89
## Residual 0.330 0.57
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.39 0.28 12.38 8.5
## ecosystem_typeLarge unconnected 0.92 0.39 10.37 2.4
## scale(day) -0.72 0.17 11.63 -4.2
## scale(water_addition_ml) 0.24 0.19 35.26 1.3
## scale(baseline) 0.15 0.19 9.84 0.8
## ecosystem_typeLarge unconnected:scale(day) 0.06 0.25 11.46 0.3
## scale(day):scale(water_addition_ml) 0.07 0.17 38.89 0.4
## scale(day):scale(baseline) -0.06 0.12 9.38 -0.5
## Pr(>|t|)
## (Intercept) 2e-06 ***
## ecosystem_typeLarge unconnected 0.039 *
## scale(day) 0.001 **
## scale(water_addition_ml) 0.212
## scale(baseline) 0.450
## ecosystem_typeLarge unconnected:scale(day) 0.805
## scale(day):scale(water_addition_ml) 0.676
## scale(day):scale(baseline) 0.620
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.687
## scale(day) -0.031 0.072
## scl(wtr_d_) 0.320 -0.107 0.335
## scale(bsln) -0.144 0.222 0.030 0.017
## ecsys_Lu:() 0.048 -0.182 -0.663 -0.063 -0.042
## scl(d):(__) 0.314 -0.009 0.281 0.802 0.027 -0.250
## scl(dy):s() 0.028 -0.042 -0.144 0.024 -0.158 0.221 -0.003Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -2.7 0.03 ** moderateReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 131.1 152.2 -54.6 109.1 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8 -0.6 -0.1 0.5 1.7
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1.218 1.10
## day 0.002 0.04 -0.89
## Residual 0.331 0.58
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.39 0.28 12.60 8.5 1e-06
## ecosystem_typeLarge unconnected 0.93 0.38 10.34 2.5 0.03
## scale(day) -0.69 0.13 14.83 -5.4 8e-05
## scale(water_addition_ml) 0.25 0.19 35.29 1.3 0.21
## scale(baseline) 0.15 0.19 9.87 0.8 0.44
## scale(day):scale(water_addition_ml) 0.08 0.17 40.42 0.5 0.62
## scale(day):scale(baseline) -0.07 0.11 9.32 -0.6 0.57
##
## (Intercept) ***
## ecosystem_typeLarge unconnected *
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.691
## scale(day) 0.005 -0.067
## scl(wtr_d_) 0.325 -0.120 0.392
## scale(bsln) -0.142 0.219 0.003 0.014
## scl(d):(__) 0.338 -0.056 0.160 0.814 0.018
## scl(dy):s() 0.018 -0.002 0.004 0.039 -0.147 0.056Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3.2 0.671 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 186.7 209.6 -81.3 162.7 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8 -0.6 0.2 0.7 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-01 0.94
## day 1e-04 0.01 -1.00
## Residual 1e+00 1.10
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6.38 0.42 14.02 15.1
## ecosystem_typeLarge unconnected 0.51 0.56 10.68 0.9
## scale(day) 0.29 0.25 37.75 1.2
## scale(water_addition_ml) 0.27 0.36 40.66 0.7
## scale(baseline) 0.05 0.28 9.87 0.2
## ecosystem_typeLarge unconnected:scale(day) -0.07 0.35 36.57 -0.2
## scale(day):scale(water_addition_ml) -0.21 0.31 41.21 -0.7
## scale(day):scale(baseline) 0.33 0.16 35.50 2.0
## Pr(>|t|)
## (Intercept) 5e-10 ***
## ecosystem_typeLarge unconnected 0.38
## scale(day) 0.25
## scale(water_addition_ml) 0.46
## scale(baseline) 0.85
## ecosystem_typeLarge unconnected:scale(day) 0.83
## scale(day):scale(water_addition_ml) 0.51
## scale(day):scale(baseline) 0.05 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.668
## scale(day) 0.080 0.010
## scl(wtr_d_) 0.394 -0.143 0.427
## scale(bsln) 0.023 -0.059 -0.030 -0.059
## ecsys_Lu:() -0.013 -0.150 -0.620 -0.072 0.008
## scl(d):(__) 0.389 -0.024 0.353 0.804 -0.042 -0.300
## scl(dy):s() -0.044 0.006 0.011 -0.075 -0.106 -0.027 -0.107
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.2 0.385 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 184.7 205.8 -81.4 162.7 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8 -0.6 0.2 0.6 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-01 0.97
## day 2e-04 0.01 -1.00
## Residual 1e+00 1.10
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.38 0.42 13.99 15.1 5e-10
## ecosystem_typeLarge unconnected 0.49 0.55 10.74 0.9 0.39
## scale(day) 0.26 0.20 38.24 1.3 0.19
## scale(water_addition_ml) 0.26 0.36 40.80 0.7 0.47
## scale(baseline) 0.05 0.28 9.90 0.2 0.85
## scale(day):scale(water_addition_ml) -0.23 0.30 41.30 -0.8 0.45
## scale(day):scale(baseline) 0.33 0.16 34.71 2.0 0.05
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline) .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.678
## scale(day) 0.084 -0.105
## scl(wtr_d_) 0.394 -0.156 0.488
## scale(bsln) 0.024 -0.059 -0.032 -0.058
## scl(d):(__) 0.405 -0.076 0.222 0.822 -0.041
## scl(dy):s() -0.045 0.003 -0.007 -0.077 -0.116 -0.120
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -6.4 0.006 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -75.8 -52.8 49.9 -99.8 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.08 -0.64 -0.02 0.73 1.96
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.120
## day 4e-05 0.007 -1.00
## Residual 7e-03 0.082
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.764 0.023 20.862 33.6
## ecosystem_typeLarge unconnected 0.032 0.029 12.760 1.1
## scale(day) 0.036 0.026 12.158 1.4
## scale(water_addition_ml) -0.047 0.027 37.379 -1.7
## scale(baseline) -0.012 0.014 10.450 -0.9
## ecosystem_typeLarge unconnected:scale(day) -0.149 0.038 12.605 -3.9
## scale(day):scale(water_addition_ml) -0.005 0.025 40.826 -0.2
## scale(day):scale(baseline) 0.018 0.018 10.512 1.0
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge unconnected 0.279
## scale(day) 0.187
## scale(water_addition_ml) 0.094 .
## scale(baseline) 0.383
## ecosystem_typeLarge unconnected:scale(day) 0.002 **
## scale(day):scale(water_addition_ml) 0.847
## scale(day):scale(baseline) 0.341
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.633
## scale(day) 0.339 -0.174
## scl(wtr_d_) 0.580 -0.216 0.326
## scale(bsln) 0.204 -0.382 0.047 0.032
## ecsys_Lu:() -0.200 0.080 -0.691 -0.082 -0.010
## scl(d):(__) 0.554 -0.009 0.300 0.812 -0.064 -0.273
## scl(dy):s() 0.084 -0.017 0.266 0.034 0.154 -0.397 0.135Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.1 0.331 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -68.3 -47.3 45.2 -90.3 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.85 -0.61 -0.07 0.64 1.94
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e-02 0.25
## day 2e-04 0.01 -1.00
## Residual 7e-03 0.08
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.750 0.023 21.023 32.8 <2e-16
## ecosystem_typeLarge unconnected 0.043 0.029 12.991 1.5 0.16
## scale(day) -0.036 0.028 11.619 -1.3 0.22
## scale(water_addition_ml) -0.054 0.028 35.273 -1.9 0.06
## scale(baseline) -0.014 0.014 9.384 -1.0 0.35
## scale(day):scale(water_addition_ml) -0.021 0.025 38.997 -0.8 0.40
## scale(day):scale(baseline) -0.009 0.027 9.561 -0.4 0.73
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml) .
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.617
## scale(day) 0.249 -0.113
## scl(wtr_d_) 0.581 -0.201 0.249
## scale(bsln) 0.197 -0.380 0.038 0.025
## scl(d):(__) 0.537 0.028 0.095 0.817 -0.078
## scl(dy):s() 0.005 0.011 -0.006 0.002 0.210 0.022Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -7.7 0.003 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 768.9 791.8 -372.4 744.9 38
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.75 -0.48 -0.08 0.38 2.82
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e+04 98
## day 5e+00 2 1.00
## Residual 2e+05 395
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3661 122 17 30.0
## ecosystem_typeLarge unconnected 60 160 11 0.4
## scale(day) 252 91 40 2.8
## scale(water_addition_ml) -295 128 43 -2.3
## scale(baseline) 30 79 10 0.4
## ecosystem_typeLarge unconnected:scale(day) -490 130 40 -3.8
## scale(day):scale(water_addition_ml) -48 112 43 -0.4
## scale(day):scale(baseline) 44 63 39 0.7
## Pr(>|t|)
## (Intercept) 4e-16 ***
## ecosystem_typeLarge unconnected 0.714
## scale(day) 0.009 **
## scale(water_addition_ml) 0.026 *
## scale(baseline) 0.711
## ecosystem_typeLarge unconnected:scale(day) 5e-04 ***
## scale(day):scale(water_addition_ml) 0.672
## scale(day):scale(baseline) 0.496
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.664
## scale(day) 0.219 -0.093
## scl(wtr_d_) 0.473 -0.149 0.399
## scale(bsln) -0.217 0.354 0.024 0.083
## ecsys_Lu:() -0.104 -0.007 -0.647 -0.050 0.033
## scl(d):(__) 0.480 -0.023 0.307 0.810 0.030 -0.232
## scl(dy):s() 0.056 0.033 -0.229 0.081 0.038 0.299 0.167
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.9 0.704 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 778.4 799.4 -378.2 756.4 39
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8 -0.5 -0.1 0.6 2.7
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e+05 439
## day 6e+02 25 -0.97
## Residual 2e+05 432
## Number of obs: 50, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3591 126 18 28.4 <2e-16
## ecosystem_typeLarge unconnected 124 163 11 0.8 0.46
## scale(day) 21 89 16 0.2 0.82
## scale(water_addition_ml) -321 143 37 -2.2 0.03
## scale(baseline) 49 81 9 0.6 0.56
## scale(day):scale(water_addition_ml) -124 124 43 -1.0 0.32
## scale(day):scale(baseline) 121 80 11 1.5 0.16
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml) *
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.643
## scale(day) 0.266 -0.127
## scl(wtr_d_) 0.509 -0.152 0.414
## scale(bsln) -0.194 0.341 0.052 0.094
## scl(d):(__) 0.498 0.002 0.179 0.825 0.051
## scl(dy):s() 0.083 0.044 -0.035 0.093 0.164 0.222Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Large connected to small"
## [1] "Large unconnected"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
\(L_{S}\) vs \(L_{L}\)
ecosystem_type_selected = c("Large connected to small",
"Large connected to large")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.3 0.255 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 30.1 57.9 -3.0 6.1 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9 -0.7 0.1 0.7 2.3
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.132
## day 3e-05 0.006 -1.00
## Residual 6e-02 0.249
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 1.434 0.045 57.121
## ecosystem_typeLarge connected to small -0.008 0.063 38.515
## scale(day) 0.026 0.044 32.058
## scale(water_addition_ml) 0.065 0.054 63.330
## scale(baseline) -0.028 0.030 39.397
## ecosystem_typeLarge connected to small:scale(day) 0.113 0.066 19.963
## scale(day):scale(water_addition_ml) 0.035 0.046 68.478
## scale(day):scale(baseline) 0.048 0.032 20.662
## t value Pr(>|t|)
## (Intercept) 31.8 <2e-16 ***
## ecosystem_typeLarge connected to small -0.1 0.9
## scale(day) 0.6 0.6
## scale(water_addition_ml) 1.2 0.2
## scale(baseline) -0.9 0.4
## ecosystem_typeLarge connected to small:scale(day) 1.7 0.1
## scale(day):scale(water_addition_ml) 0.8 0.5
## scale(day):scale(baseline) 1.5 0.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lcts scl(d) sc(__) scl(b) e_Lcts: s():(_
## ecsyst_Lcts -0.537
## scale(day) 0.031 0.054
## scl(wtr_d_) 0.412 -0.030 0.467
## scale(bsln) -0.088 0.114 -0.113 -0.183
## ecs_Lcts:() 0.014 -0.058 -0.574 -0.138 0.031
## scl(d):(__) 0.603 -0.126 0.141 0.733 -0.064 -0.025
## scl(dy):s() -0.128 0.032 -0.027 -0.072 -0.055 0.108 -0.209
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2 0.943 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 30.8 56.3 -4.4 8.8 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.86 -0.80 0.07 0.70 2.36
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-02 0.23
## day 1e-04 0.01 -1.00
## Residual 6e-02 0.25
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.427 0.046 53.161 31.3
## ecosystem_typeLarge connected to small 0.005 0.064 38.685 0.1
## scale(day) 0.069 0.039 25.653 1.8
## scale(water_addition_ml) 0.073 0.054 61.824 1.4
## scale(baseline) -0.030 0.031 31.678 -1.0
## scale(day):scale(water_addition_ml) 0.031 0.047 65.760 0.7
## scale(day):scale(baseline) 0.043 0.034 16.604 1.3
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to small 0.94
## scale(day) 0.08 .
## scale(water_addition_ml) 0.18
## scale(baseline) 0.34
## scale(day):scale(water_addition_ml) 0.51
## scale(day):scale(baseline) 0.22
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lcts scl(d) sc(__) scl(b) s():(_
## ecsyst_Lcts -0.537
## scale(day) 0.012 0.020
## scl(wtr_d_) 0.418 -0.044 0.455
## scale(bsln) -0.087 0.117 -0.112 -0.182
## scl(d):(__) 0.605 -0.131 0.141 0.731 -0.061
## scl(dy):s() -0.123 0.036 0.040 -0.053 -0.111 -0.196
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 2.9 0.565 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 192.0 219.8 -84.0 168.0 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.69 -0.73 -0.09 0.64 2.42
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.921 0.96
## day 0.001 0.04 -1.00
## Residual 0.473 0.69
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 2e+00 1e-01 2e+01
## ecosystem_typeLarge connected to small -1e-01 2e-01 2e+01
## scale(day) -6e-01 1e-01 2e+01
## scale(water_addition_ml) 1e-01 1e-01 6e+01
## scale(baseline) 5e-04 1e-01 1e+01
## ecosystem_typeLarge connected to small:scale(day) -1e-01 2e-01 2e+01
## scale(day):scale(water_addition_ml) 4e-02 1e-01 6e+01
## scale(day):scale(baseline) -9e-02 1e-01 2e+01
## t value Pr(>|t|)
## (Intercept) 16.9 5e-15 ***
## ecosystem_typeLarge connected to small -0.5 0.6
## scale(day) -4.6 1e-04 ***
## scale(water_addition_ml) 0.8 0.4
## scale(baseline) 0.0 1.0
## ecosystem_typeLarge connected to small:scale(day) -0.7 0.5
## scale(day):scale(water_addition_ml) 0.3 0.7
## scale(day):scale(baseline) -0.9 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lcts scl(d) sc(__) scl(b) e_Lcts: s():(_
## ecsyst_Lcts -0.546
## scale(day) -0.235 0.211
## scl(wtr_d_) 0.321 0.001 0.424
## scale(bsln) 0.010 -0.010 -0.009 -0.003
## ecs_Lcts:() 0.184 -0.358 -0.575 -0.117 0.006
## scl(d):(__) 0.504 -0.096 0.093 0.705 0.012 0.010
## scl(dy):s() -0.031 0.010 0.011 -0.021 -0.349 -0.012 -0.057
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.3 0.409 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 190.5 216.0 -84.2 168.5 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7 -0.7 -0.1 0.7 2.3
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.958 0.98
## day 0.001 0.04 -1.00
## Residual 0.476 0.69
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3e+00 1e-01 3e+01 17.3
## ecosystem_typeLarge connected to small -2e-01 2e-01 2e+01 -0.8
## scale(day) -7e-01 1e-01 2e+01 -6.1
## scale(water_addition_ml) 1e-01 1e-01 6e+01 0.7
## scale(baseline) 8e-04 1e-01 1e+01 0.0
## scale(day):scale(water_addition_ml) 4e-02 1e-01 6e+01 0.3
## scale(day):scale(baseline) -9e-02 1e-01 1e+01 -0.9
## Pr(>|t|)
## (Intercept) 3e-16 ***
## ecosystem_typeLarge connected to small 0.4
## scale(day) 3e-06 ***
## scale(water_addition_ml) 0.5
## scale(baseline) 1.0
## scale(day):scale(water_addition_ml) 0.8
## scale(day):scale(baseline) 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lcts scl(d) sc(__) scl(b) s():(_
## ecsyst_Lcts -0.523
## scale(day) -0.164 0.007
## scl(wtr_d_) 0.352 -0.045 0.436
## scale(bsln) 0.010 -0.009 -0.007 -0.003
## scl(d):(__) 0.513 -0.100 0.120 0.710 0.012
## scl(dy):s() -0.029 0.006 0.005 -0.023 -0.353 -0.056
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3.6 0.8 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 272.9 300.7 -124.4 248.9 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.57 -0.03 0.73 2.48
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.566
## day 6e-06 0.003 -1.00
## Residual 1e+00 1.190
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 6.3 0.3 23.6
## ecosystem_typeLarge connected to small 0.2 0.4 15.0
## scale(day) 0.2 0.2 62.0
## scale(water_addition_ml) 0.6 0.3 62.2
## scale(baseline) -0.1 0.2 15.6
## ecosystem_typeLarge connected to small:scale(day) 0.1 0.3 59.5
## scale(day):scale(water_addition_ml) 0.2 0.2 65.0
## scale(day):scale(baseline) 0.2 0.1 60.1
## t value Pr(>|t|)
## (Intercept) 23.3 <2e-16 ***
## ecosystem_typeLarge connected to small 0.6 0.58
## scale(day) 1.0 0.33
## scale(water_addition_ml) 2.3 0.03 *
## scale(baseline) -0.6 0.58
## ecosystem_typeLarge connected to small:scale(day) 0.3 0.75
## scale(day):scale(water_addition_ml) 1.1 0.29
## scale(day):scale(baseline) 1.7 0.10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lcts scl(d) sc(__) scl(b) e_Lcts: s():(_
## ecsyst_Lcts -0.547
## scale(day) 0.010 0.068
## scl(wtr_d_) 0.324 0.019 0.478
## scale(bsln) 0.062 -0.160 -0.122 -0.167
## ecs_Lcts:() 0.044 -0.049 -0.585 -0.126 0.047
## scl(d):(__) 0.495 -0.084 0.117 0.737 -0.043 0.042
## scl(dy):s() -0.145 0.047 0.141 -0.071 -0.043 -0.188 -0.268
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.7 0.559 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 271.0 296.4 -124.5 249.0 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.57 -0.06 0.75 2.51
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.585
## day 1e-05 0.003 -1.00
## Residual 1e+00 1.190
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6.3 0.3 23.6 23.2
## ecosystem_typeLarge connected to small 0.2 0.4 15.1 0.6
## scale(day) 0.2 0.2 62.1 1.5
## scale(water_addition_ml) 0.6 0.3 62.0 2.4
## scale(baseline) -0.1 0.2 15.6 -0.6
## scale(day):scale(water_addition_ml) 0.2 0.2 64.8 1.1
## scale(day):scale(baseline) 0.3 0.1 59.9 1.8
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to small 0.56
## scale(day) 0.15
## scale(water_addition_ml) 0.02 *
## scale(baseline) 0.57
## scale(day):scale(water_addition_ml) 0.29
## scale(day):scale(baseline) 0.08 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lcts scl(d) sc(__) scl(b) s():(_
## ecsyst_Lcts -0.546
## scale(day) 0.041 0.047
## scl(wtr_d_) 0.332 0.012 0.502
## scale(bsln) 0.060 -0.158 -0.116 -0.162
## scl(d):(__) 0.493 -0.081 0.175 0.748 -0.045
## scl(dy):s() -0.139 0.038 0.039 -0.097 -0.040 -0.265
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.325 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -110.1 -82.3 67.1 -134.1 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1 -0.6 0.2 0.6 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-03 0.037
## day 4e-06 0.002 -1.00
## Residual 1e-02 0.098
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 0.787 0.018 69.484
## ecosystem_typeLarge connected to small -0.009 0.026 60.527
## scale(day) 0.001 0.018 26.044
## scale(water_addition_ml) -0.014 0.021 71.192
## scale(baseline) -0.004 0.012 59.822
## ecosystem_typeLarge connected to small:scale(day) 0.042 0.027 15.842
## scale(day):scale(water_addition_ml) 0.002 0.018 69.912
## scale(day):scale(baseline) 0.009 0.013 14.963
## t value Pr(>|t|)
## (Intercept) 44.5 <2e-16 ***
## ecosystem_typeLarge connected to small -0.3 0.7
## scale(day) 0.1 0.9
## scale(water_addition_ml) -0.6 0.5
## scale(baseline) -0.3 0.7
## ecosystem_typeLarge connected to small:scale(day) 1.5 0.1
## scale(day):scale(water_addition_ml) 0.1 0.9
## scale(day):scale(baseline) 0.7 0.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lcts scl(d) sc(__) scl(b) e_Lcts: s():(_
## ecsyst_Lcts -0.553
## scale(day) 0.039 0.057
## scl(wtr_d_) 0.390 0.013 0.448
## scale(bsln) -0.186 0.377 0.039 0.052
## ecs_Lcts:() 0.024 -0.024 -0.600 -0.117 -0.013
## scl(d):(__) 0.587 -0.106 0.122 0.742 0.003 0.022
## scl(dy):s() 0.040 -0.013 -0.214 0.005 0.001 0.378 0.062
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.9 0.77 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -109.9 -84.5 66.0 -131.9 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1 -0.5 0.2 0.6 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-03 0.071
## day 1e-05 0.004 -1.00
## Residual 1e-02 0.098
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 8e-01 2e-02 7e+01 44.1
## ecosystem_typeLarge connected to small -8e-03 3e-02 6e+01 -0.3
## scale(day) 2e-02 1e-02 2e+01 1.1
## scale(water_addition_ml) -1e-02 2e-02 7e+01 -0.5
## scale(baseline) -4e-03 1e-02 6e+01 -0.3
## scale(day):scale(water_addition_ml) 9e-05 2e-02 7e+01 0.0
## scale(day):scale(baseline) 2e-03 1e-02 1e+01 0.1
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to small 0.8
## scale(day) 0.3
## scale(water_addition_ml) 0.6
## scale(baseline) 0.7
## scale(day):scale(water_addition_ml) 1.0
## scale(day):scale(baseline) 0.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lcts scl(d) sc(__) scl(b) s():(_
## ecsyst_Lcts -0.552
## scale(day) 0.067 0.052
## scl(wtr_d_) 0.400 0.010 0.456
## scale(bsln) -0.185 0.377 0.038 0.052
## scl(d):(__) 0.593 -0.108 0.162 0.750 0.003
## scl(dy):s() 0.032 -0.004 0.016 0.050 0.011 0.055
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 3.8 0.883 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1183.6 1211.4 -579.8 1159.6 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.98 -0.71 -0.03 0.51 2.44
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e+04 306
## day 5e+02 22 -1.00
## Residual 3e+05 527
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 3815 104 34
## ecosystem_typeLarge connected to small -74 149 22
## scale(day) 326 99 35
## scale(water_addition_ml) -169 120 73
## scale(baseline) 10 70 21
## ecosystem_typeLarge connected to small:scale(day) -22 149 24
## scale(day):scale(water_addition_ml) -10 102 72
## scale(day):scale(baseline) -56 70 23
## t value Pr(>|t|)
## (Intercept) 36.8 <2e-16 ***
## ecosystem_typeLarge connected to small -0.5 0.623
## scale(day) 3.3 0.002 **
## scale(water_addition_ml) -1.4 0.163
## scale(baseline) 0.1 0.891
## ecosystem_typeLarge connected to small:scale(day) -0.1 0.883
## scale(day):scale(water_addition_ml) -0.1 0.925
## scale(day):scale(baseline) -0.8 0.429
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lcts scl(d) sc(__) scl(b) e_Lcts: s():(_
## ecsyst_Lcts -0.532
## scale(day) 0.226 -0.074
## scl(wtr_d_) 0.413 -0.015 0.442
## scale(bsln) 0.022 -0.036 0.016 0.021
## ecs_Lcts:() -0.103 0.200 -0.573 -0.121 -0.012
## scl(d):(__) 0.571 -0.103 0.167 0.777 0.010 -0.015
## scl(dy):s() 0.073 -0.022 0.032 0.085 0.221 -0.036 0.119
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.633 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1181.6 1207.1 -579.8 1159.6 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.97 -0.72 -0.06 0.51 2.45
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e+04 306
## day 5e+02 22 -1.00
## Residual 3e+05 527
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3813 103 38 37.0
## ecosystem_typeLarge connected to small -70 146 28 -0.5
## scale(day) 317 81 35 3.9
## scale(water_addition_ml) -171 119 72 -1.4
## scale(baseline) 10 70 21 0.1
## scale(day):scale(water_addition_ml) -10 102 72 -0.1
## scale(day):scale(baseline) -57 70 23 -0.8
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to small 0.6
## scale(day) 4e-04 ***
## scale(water_addition_ml) 0.2
## scale(baseline) 0.9
## scale(day):scale(water_addition_ml) 0.9
## scale(day):scale(baseline) 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lcts scl(d) sc(__) scl(b) s():(_
## ecsyst_Lcts -0.525
## scale(day) 0.204 0.050
## scl(wtr_d_) 0.406 0.009 0.458
## scale(bsln) 0.021 -0.034 0.011 0.020
## scl(d):(__) 0.573 -0.102 0.193 0.781 0.010
## scl(dy):s() 0.069 -0.015 0.014 0.082 0.220 0.119
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Large connected to small"
## [1] "Large connected to large"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
\(L_{L}\) vs \(L\)
ecosystem_type_selected = c("Large connected to large",
"Large unconnected")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -3.2 0.028 ** moderateFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 15.4 43.2 4.3 -8.6 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.56 0.08 0.75 1.58
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-02 0.21
## day 1e-04 0.01 -0.99
## Residual 5e-02 0.22
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.448 0.046 35.013 31.2
## ecosystem_typeLarge unconnected 0.088 0.059 14.058 1.5
## scale(day) 0.028 0.045 28.477 0.6
## scale(water_addition_ml) 0.058 0.061 60.982 1.0
## scale(baseline) 0.014 0.028 13.542 0.5
## ecosystem_typeLarge unconnected:scale(day) -0.185 0.066 15.987 -2.8
## scale(day):scale(water_addition_ml) 0.045 0.050 64.543 0.9
## scale(day):scale(baseline) 0.003 0.031 14.701 0.1
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge unconnected 0.16
## scale(day) 0.54
## scale(water_addition_ml) 0.34
## scale(baseline) 0.61
## ecosystem_typeLarge unconnected:scale(day) 0.01 *
## scale(day):scale(water_addition_ml) 0.37
## scale(day):scale(baseline) 0.92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.514
## scale(day) 0.287 -0.113
## scl(wtr_d_) 0.626 -0.218 0.571
## scale(bsln) -0.020 -0.188 -0.105 -0.178
## ecsys_Lu:() -0.134 -0.028 -0.516 -0.139 0.038
## scl(d):(__) 0.706 -0.137 0.396 0.823 -0.154 -0.226
## scl(dy):s() -0.070 0.026 0.069 -0.084 -0.030 -0.209 -0.091Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1 0.311 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 19.6 45.0 1.2 -2.4 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.60 0.05 0.85 1.41
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-01 0.37
## day 3e-04 0.02 -0.99
## Residual 5e-02 0.22
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.43 0.05 33.62 30.0 <2e-16
## ecosystem_typeLarge unconnected 0.08 0.06 14.22 1.3 0.2
## scale(day) -0.04 0.04 28.75 -0.9 0.4
## scale(water_addition_ml) 0.03 0.06 60.01 0.5 0.6
## scale(baseline) 0.02 0.03 13.45 0.6 0.5
## scale(day):scale(water_addition_ml) 0.01 0.05 63.99 0.2 0.8
## scale(day):scale(baseline) -0.01 0.04 15.29 -0.4 0.7
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.523
## scale(day) 0.205 -0.129
## scl(wtr_d_) 0.614 -0.221 0.519
## scale(bsln) -0.011 -0.189 -0.086 -0.171
## scl(d):(__) 0.696 -0.146 0.291 0.819 -0.146
## scl(dy):s() -0.084 0.017 -0.033 -0.097 -0.053 -0.121Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.6 0.101 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 196.2 224.0 -86.1 172.2 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.90 -0.72 -0.07 0.43 2.66
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.829 0.91
## day 0.001 0.04 -0.82
## Residual 0.400 0.63
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.67 0.21 24.11 12.5
## ecosystem_typeLarge unconnected 0.71 0.33 15.39 2.2
## scale(day) -0.48 0.14 29.91 -3.5
## scale(water_addition_ml) 0.44 0.19 60.41 2.3
## scale(baseline) 0.02 0.15 14.74 0.1
## ecosystem_typeLarge unconnected:scale(day) -0.18 0.20 16.88 -0.9
## scale(day):scale(water_addition_ml) 0.28 0.15 61.86 1.8
## scale(day):scale(baseline) -0.10 0.09 15.01 -1.1
## Pr(>|t|)
## (Intercept) 5e-12 ***
## ecosystem_typeLarge unconnected 0.046 *
## scale(day) 0.002 **
## scale(water_addition_ml) 0.025 *
## scale(baseline) 0.907
## ecosystem_typeLarge unconnected:scale(day) 0.392
## scale(day):scale(water_addition_ml) 0.080 .
## scale(day):scale(baseline) 0.288
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.555
## scale(day) 0.206 -0.075
## scl(wtr_d_) 0.438 -0.147 0.589
## scale(bsln) -0.059 0.116 -0.004 -0.007
## ecsys_Lu:() -0.104 -0.018 -0.519 -0.170 -0.006
## scl(d):(__) 0.488 -0.099 0.422 0.831 0.002 -0.260
## scl(dy):s() -0.030 -0.001 -0.071 -0.042 -0.036 0.132 -0.070Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -1.8 0.05 * weakReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 195.0 220.5 -86.5 173.0 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.98 -0.71 0.01 0.44 2.49
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.930 0.96
## day 0.001 0.04 -0.85
## Residual 0.400 0.63
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.65 0.21 23.57 12.4 8e-12
## ecosystem_typeLarge unconnected 0.70 0.33 15.43 2.1 0.05
## scale(day) -0.55 0.12 33.02 -4.5 7e-05
## scale(water_addition_ml) 0.41 0.19 61.80 2.2 0.03
## scale(baseline) 0.02 0.15 14.74 0.1 0.91
## scale(day):scale(water_addition_ml) 0.24 0.15 63.68 1.6 0.12
## scale(day):scale(baseline) -0.09 0.09 14.92 -1.0 0.35
##
## (Intercept) ***
## ecosystem_typeLarge unconnected *
## scale(day) ***
## scale(water_addition_ml) *
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.560
## scale(day) 0.168 -0.099
## scl(wtr_d_) 0.432 -0.155 0.587
## scale(bsln) -0.060 0.116 -0.008 -0.009
## scl(d):(__) 0.483 -0.112 0.342 0.826 0.000
## scl(dy):s() -0.017 0.002 -0.002 -0.020 -0.052 -0.036Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.2 0.243 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 257.1 285.0 -116.6 233.1 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.92 -0.57 -0.01 0.55 2.45
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.536
## day 4e-06 0.002 -1.00
## Residual 1e+00 1.064
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6.54 0.27 30.09 23.8
## ecosystem_typeLarge unconnected 0.68 0.39 14.98 1.7
## scale(day) 0.19 0.20 63.71 0.9
## scale(water_addition_ml) 0.68 0.31 62.75 2.2
## scale(baseline) 0.13 0.19 15.15 0.7
## ecosystem_typeLarge unconnected:scale(day) -0.13 0.28 60.05 -0.5
## scale(day):scale(water_addition_ml) 0.43 0.25 65.24 1.7
## scale(day):scale(baseline) 0.04 0.13 59.74 0.3
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge unconnected 0.10
## scale(day) 0.36
## scale(water_addition_ml) 0.03 *
## scale(baseline) 0.50
## ecosystem_typeLarge unconnected:scale(day) 0.65
## scale(day):scale(water_addition_ml) 0.09 .
## scale(day):scale(baseline) 0.74
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.535
## scale(day) 0.280 -0.096
## scl(wtr_d_) 0.529 -0.154 0.634
## scale(bsln) 0.040 -0.211 -0.117 -0.169
## ecsys_Lu:() -0.134 0.000 -0.505 -0.164 0.022
## scl(d):(__) 0.599 -0.106 0.440 0.832 -0.112 -0.244
## scl(dy):s() -0.110 0.013 0.069 -0.106 -0.009 -0.180 -0.189
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.6 0.105 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 255.4 280.8 -116.7 233.4 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.92 -0.56 -0.03 0.53 2.42
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.548
## day 6e-06 0.003 -1.00
## Residual 1e+00 1.065
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.52 0.27 28.80 23.9 <2e-16
## ecosystem_typeLarge unconnected 0.68 0.39 15.00 1.7 0.11
## scale(day) 0.14 0.17 64.25 0.8 0.42
## scale(water_addition_ml) 0.65 0.30 62.97 2.2 0.03
## scale(baseline) 0.13 0.19 15.17 0.7 0.50
## scale(day):scale(water_addition_ml) 0.40 0.24 65.02 1.7 0.10
## scale(day):scale(baseline) 0.03 0.13 59.92 0.3 0.80
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml) *
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.540
## scale(day) 0.246 -0.111
## scl(wtr_d_) 0.518 -0.157 0.648
## scale(bsln) 0.043 -0.211 -0.123 -0.167
## scl(d):(__) 0.588 -0.110 0.378 0.827 -0.109
## scl(dy):s() -0.137 0.014 -0.026 -0.140 -0.009 -0.244
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -3.6 0.023 ** moderateFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -125.3 -97.5 74.7 -149.3 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3 -0.5 0.3 0.6 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.112
## day 4e-05 0.006 -1.00
## Residual 7e-03 0.084
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 8e-01 2e-02 6e+01 43.4
## ecosystem_typeLarge unconnected -2e-04 2e-02 5e+01 0.0
## scale(day) 7e-03 2e-02 3e+01 0.4
## scale(water_addition_ml) -2e-02 2e-02 7e+01 -0.6
## scale(baseline) 2e-02 1e-02 5e+01 2.0
## ecosystem_typeLarge unconnected:scale(day) -9e-02 3e-02 2e+01 -3.1
## scale(day):scale(water_addition_ml) -7e-03 2e-02 7e+01 -0.4
## scale(day):scale(baseline) 2e-02 1e-02 2e+01 1.2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge unconnected 0.993
## scale(day) 0.726
## scale(water_addition_ml) 0.525
## scale(baseline) 0.048 *
## ecosystem_typeLarge unconnected:scale(day) 0.007 **
## scale(day):scale(water_addition_ml) 0.709
## scale(day):scale(baseline) 0.257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.526
## scale(day) 0.394 -0.222
## scl(wtr_d_) 0.652 -0.268 0.526
## scale(bsln) -0.020 -0.053 0.015 -0.002
## ecsys_Lu:() -0.216 0.168 -0.528 -0.144 0.014
## scl(d):(__) 0.728 -0.178 0.373 0.828 -0.064 -0.225
## scl(dy):s() 0.041 0.004 0.006 -0.005 0.139 -0.068 0.065
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.622 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -120.0 -94.5 71.0 -142.0 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3 -0.5 0.2 0.6 2.1
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-02 0.174
## day 9e-05 0.009 -1.00
## Residual 7e-03 0.084
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.77 0.02 61.38 43.0 <2e-16
## ecosystem_typeLarge unconnected 0.01 0.02 57.37 0.6 0.56
## scale(day) -0.02 0.02 24.97 -1.2 0.23
## scale(water_addition_ml) -0.02 0.02 64.42 -1.0 0.33
## scale(baseline) 0.02 0.01 36.26 2.0 0.05
## scale(day):scale(water_addition_ml) -0.02 0.02 68.33 -0.9 0.38
## scale(day):scale(baseline) 0.01 0.02 15.11 0.8 0.45
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline) .
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.500
## scale(day) 0.341 -0.139
## scl(wtr_d_) 0.651 -0.251 0.459
## scale(bsln) -0.020 -0.056 0.023 -0.002
## scl(d):(__) 0.721 -0.143 0.264 0.828 -0.065
## scl(dy):s() 0.023 0.013 -0.024 -0.011 0.212 0.042
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -5.5 0.009 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1163.6 1191.4 -569.8 1139.6 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.77 -0.66 -0.05 0.42 3.01
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+05 560
## day 1e+03 34 -1.00
## Residual 2e+05 444
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3843.1 103.4 44.0 37.2
## ecosystem_typeLarge unconnected -118.9 134.1 24.6 -0.9
## scale(day) 427.8 105.0 27.9 4.1
## scale(water_addition_ml) 0.1 130.2 71.4 0.0
## scale(baseline) 34.8 61.8 22.8 0.6
## ecosystem_typeLarge unconnected:scale(day) -562.6 159.8 17.5 -3.5
## scale(day):scale(water_addition_ml) 70.7 105.9 72.9 0.7
## scale(day):scale(baseline) -54.1 74.4 16.5 -0.7
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge unconnected 0.384
## scale(day) 3e-04 ***
## scale(water_addition_ml) 0.999
## scale(baseline) 0.579
## ecosystem_typeLarge unconnected:scale(day) 0.003 **
## scale(day):scale(water_addition_ml) 0.506
## scale(day):scale(baseline) 0.478
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) e_Lu:( s():(_
## ecsystm_tLu -0.542
## scale(day) 0.508 -0.303
## scl(wtr_d_) 0.630 -0.240 0.522
## scale(bsln) -0.110 0.217 -0.033 0.002
## ecsys_Lu:() -0.283 0.365 -0.542 -0.143 0.087
## scl(d):(__) 0.697 -0.177 0.381 0.849 -0.026 -0.201
## scl(dy):s() 0.005 0.077 -0.109 0.024 0.351 0.206 0.062
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.682 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1170.9 1196.4 -574.5 1148.9 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.48 -0.65 -0.08 0.47 2.96
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e+05 953
## day 3e+03 55 -1.00
## Residual 2e+05 448
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3764 103 45 36.4 <2e-16
## ecosystem_typeLarge unconnected 62 124 48 0.5 0.62
## scale(day) 240 110 23 2.2 0.04
## scale(water_addition_ml) -19 134 67 -0.1 0.89
## scale(baseline) 55 65 15 0.8 0.41
## scale(day):scale(water_addition_ml) 40 108 70 0.4 0.72
## scale(day):scale(baseline) 3 97 15 0.0 0.97
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## scale(day) *
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu scl(d) sc(__) scl(b) s():(_
## ecsystm_tLu -0.472
## scale(day) 0.485 -0.114
## scl(wtr_d_) 0.622 -0.205 0.443
## scale(bsln) -0.079 0.186 0.013 0.014
## scl(d):(__) 0.679 -0.111 0.276 0.850 -0.007
## scl(dy):s() 0.053 0.002 0.003 0.044 0.474 0.085
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Large connected to large"
## [1] "Large unconnected"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
\(M_{M}\) vs \(M\)
ecosystem_type_selected = c("Medium unconnected",
"Medium connected to medium")Shannon
response_variable_selected = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.8 0.206 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 38.5 66.3 -7.2 14.5 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.44 -0.62 0.02 0.66 2.31
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e-02 0.24
## day 1e-04 0.01 -1.00
## Residual 7e-02 0.26
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.321 0.048 58.619 27.7
## ecosystem_typeMedium unconnected 0.013 0.069 43.379 0.2
## scale(day) 0.004 0.049 31.165 0.1
## scale(water_addition_ml) -0.050 0.053 67.973 -0.9
## scale(baseline) 0.060 0.032 40.778 1.9
## ecosystem_typeMedium unconnected:scale(day) 0.133 0.074 21.173 1.8
## scale(day):scale(water_addition_ml) 0.022 0.043 69.502 0.5
## scale(day):scale(baseline) 0.013 0.035 21.012 0.4
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeMedium unconnected 0.85
## scale(day) 0.94
## scale(water_addition_ml) 0.35
## scale(baseline) 0.07 .
## ecosystem_typeMedium unconnected:scale(day) 0.09 .
## scale(day):scale(water_addition_ml) 0.61
## scale(day):scale(baseline) 0.71
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) e_Mu:( s():(_
## ecsystm_tMu -0.602
## scale(day) 0.009 0.018
## scl(wtr_d_) 0.416 -0.180 0.478
## scale(bsln) -0.129 0.176 -0.002 -0.061
## ecsys_Mu:() 0.024 -0.108 -0.593 -0.185 -0.016
## scl(d):(__) 0.593 -0.250 0.163 0.696 -0.093 -0.059
## scl(dy):s() -0.091 0.023 -0.144 -0.174 -0.114 0.179 -0.169
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.8 0.651 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 39.4 64.9 -8.7 17.4 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.42 -0.53 0.01 0.68 2.25
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-01 0.32
## day 2e-04 0.01 -1.00
## Residual 7e-02 0.26
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.315 0.048 55.798 27.2 <2e-16
## ecosystem_typeMedium unconnected 0.033 0.070 47.495 0.5 0.64
## scale(day) 0.056 0.042 25.836 1.3 0.20
## scale(water_addition_ml) -0.034 0.052 67.673 -0.6 0.52
## scale(baseline) 0.062 0.033 34.979 1.9 0.07
## scale(day):scale(water_addition_ml) 0.025 0.044 68.341 0.6 0.58
## scale(day):scale(baseline) 0.002 0.037 17.944 0.1 0.95
##
## (Intercept) ***
## ecosystem_typeMedium unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline) .
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) s():(_
## ecsystm_tMu -0.602
## scale(day) -0.011 -0.060
## scl(wtr_d_) 0.427 -0.213 0.444
## scale(bsln) -0.128 0.174 -0.014 -0.065
## scl(d):(__) 0.595 -0.262 0.148 0.692 -0.094
## scl(dy):s() -0.090 0.041 -0.043 -0.136 -0.172 -0.150
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Biomass
response_variable_selected = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -5.6 0.008 *** strongFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 222.1 249.9 -99.1 198.1 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.64 -0.49 0.01 0.53 2.38
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-01 0.71
## day 2e-04 0.02 -1.00
## Residual 7e-01 0.84
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.460 0.196 22.189 12.6
## ecosystem_typeMedium unconnected -0.973 0.305 14.940 -3.2
## scale(day) -1.094 0.148 52.607 -7.4
## scale(water_addition_ml) 0.062 0.169 61.036 0.4
## scale(baseline) -0.176 0.143 14.378 -1.2
## ecosystem_typeMedium unconnected:scale(day) 0.524 0.218 45.976 2.4
## scale(day):scale(water_addition_ml) -0.319 0.142 64.436 -2.2
## scale(day):scale(baseline) -0.005 0.104 46.664 0.0
## Pr(>|t|)
## (Intercept) 1e-11 ***
## ecosystem_typeMedium unconnected 0.006 **
## scale(day) 1e-09 ***
## scale(water_addition_ml) 0.713
## scale(baseline) 0.239
## ecosystem_typeMedium unconnected:scale(day) 0.020 *
## scale(day):scale(water_addition_ml) 0.028 *
## scale(day):scale(baseline) 0.964
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) e_Mu:( s():(_
## ecsystm_tMu -0.585
## scale(day) -0.059 0.055
## scl(wtr_d_) 0.319 -0.118 0.487
## scale(bsln) 0.025 -0.069 -0.063 -0.090
## ecsys_Mu:() 0.077 -0.157 -0.586 -0.164 0.033
## scl(d):(__) 0.469 -0.174 0.131 0.682 -0.028 -0.010
## scl(dy):s() -0.110 0.050 0.047 -0.096 -0.161 -0.085 -0.221
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -2.2 0.039 ** moderateReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 225.4 250.9 -101.7 203.4 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.5 0.0 0.5 2.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-01 0.97
## day 8e-04 0.03 -1.00
## Residual 7e-01 0.86
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.40 0.20 22.69 11.9 3e-11
## ecosystem_typeMedium unconnected -0.79 0.30 16.98 -2.6 0.02
## scale(day) -0.88 0.13 38.38 -6.9 4e-08
## scale(water_addition_ml) 0.14 0.17 59.83 0.8 0.43
## scale(baseline) -0.19 0.15 13.47 -1.3 0.22
## scale(day):scale(water_addition_ml) -0.32 0.15 62.16 -2.2 0.03
## scale(day):scale(baseline) 0.02 0.11 29.60 0.2 0.88
##
## (Intercept) ***
## ecosystem_typeMedium unconnected *
## scale(day) ***
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml) *
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) s():(_
## ecsystm_tMu -0.574
## scale(day) -0.089 -0.055
## scl(wtr_d_) 0.340 -0.165 0.476
## scale(bsln) 0.021 -0.061 -0.051 -0.085
## scl(d):(__) 0.470 -0.181 0.141 0.678 -0.027
## scl(dy):s() -0.098 0.035 -0.001 -0.103 -0.267 -0.213
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Richness
response_variable_selected = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.1 0.13 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 303.9 331.7 -140.0 279.9 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.91 -0.67 0.01 0.66 2.66
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-01 0.95
## day 6e-04 0.02 -1.00
## Residual 2e+00 1.50
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6e+00 3e-01 2e+01 20.4
## ecosystem_typeMedium unconnected -1e+00 5e-01 2e+01 -2.1
## scale(day) -2e-01 3e-01 5e+01 -0.8
## scale(water_addition_ml) -4e-04 3e-01 6e+01 0.0
## scale(baseline) 2e-01 2e-01 1e+01 1.1
## ecosystem_typeMedium unconnected:scale(day) 3e-01 4e-01 4e+01 0.7
## scale(day):scale(water_addition_ml) -1e-01 2e-01 7e+01 -0.5
## scale(day):scale(baseline) -4e-02 2e-01 4e+01 -0.2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeMedium unconnected 0.05 *
## scale(day) 0.40
## scale(water_addition_ml) 1.00
## scale(baseline) 0.30
## ecosystem_typeMedium unconnected:scale(day) 0.48
## scale(day):scale(water_addition_ml) 0.59
## scale(day):scale(baseline) 0.81
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) e_Mu:( s():(_
## ecsystm_tMu -0.588
## scale(day) -0.005 0.024
## scl(wtr_d_) 0.361 -0.139 0.488
## scale(bsln) 0.024 -0.077 -0.041 -0.066
## ecsys_Mu:() 0.045 -0.105 -0.585 -0.163 0.022
## scl(d):(__) 0.522 -0.199 0.143 0.689 -0.036 -0.018
## scl(dy):s() -0.087 0.041 0.029 -0.094 -0.108 -0.085 -0.157
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -1.6 0.058 * weakReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 302.4 327.9 -140.2 280.4 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.85 -0.70 -0.05 0.63 2.57
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e+00 1.02
## day 7e-04 0.03 -1.00
## Residual 2e+00 1.50
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.23 0.31 25.39 20.3 <2e-16
## ecosystem_typeMedium unconnected -0.95 0.46 16.38 -2.1 0.06
## scale(day) -0.11 0.21 48.90 -0.5 0.60
## scale(water_addition_ml) 0.04 0.29 62.27 0.1 0.90
## scale(baseline) 0.23 0.22 14.38 1.0 0.31
## scale(day):scale(water_addition_ml) -0.13 0.25 65.43 -0.5 0.59
## scale(day):scale(baseline) -0.03 0.18 41.07 -0.2 0.85
##
## (Intercept) ***
## ecosystem_typeMedium unconnected .
## scale(day)
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) s():(_
## ecsystm_tMu -0.586
## scale(day) 0.017 -0.048
## scl(wtr_d_) 0.372 -0.161 0.490
## scale(bsln) 0.023 -0.075 -0.034 -0.063
## scl(d):(__) 0.521 -0.202 0.161 0.693 -0.035
## scl(dy):s() -0.082 0.032 -0.025 -0.109 -0.121 -0.158
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Evenness
response_variable_selected = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -0.8 0.089 * weakFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -82.6 -54.8 53.3 -106.6 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.61 -0.72 0.09 0.77 1.97
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-14 1e-07
## day 2e-17 5e-09 -1.00
## Residual 1e-02 1e-01
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.758 0.021 75.000 35.4
## ecosystem_typeMedium unconnected 0.067 0.032 75.000 2.1
## scale(day) 0.031 0.021 75.000 1.5
## scale(water_addition_ml) 0.003 0.024 75.000 0.1
## scale(baseline) -0.007 0.015 75.000 -0.5
## ecosystem_typeMedium unconnected:scale(day) 0.027 0.032 75.000 0.8
## scale(day):scale(water_addition_ml) 0.043 0.019 75.000 2.2
## scale(day):scale(baseline) -0.019 0.015 75.000 -1.3
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeMedium unconnected 0.04 *
## scale(day) 0.15
## scale(water_addition_ml) 0.92
## scale(baseline) 0.62
## ecosystem_typeMedium unconnected:scale(day) 0.41
## scale(day):scale(water_addition_ml) 0.03 *
## scale(day):scale(baseline) 0.21
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) e_Mu:( s():(_
## ecsystm_tMu -0.621
## scale(day) 0.104 -0.039
## scl(wtr_d_) 0.415 -0.172 0.516
## scale(bsln) -0.223 0.352 0.023 -0.018
## ecsys_Mu:() -0.040 0.015 -0.621 -0.223 -0.011
## scl(d):(__) 0.599 -0.261 0.181 0.702 -0.103 -0.070
## scl(dy):s() -0.059 0.024 -0.266 -0.181 -0.001 0.366 -0.101
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 -2.1 0.042 ** moderateReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## -83.9 -58.4 53.0 -105.9 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.72 -0.66 0.04 0.77 1.99
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-12 2e-06
## day 6e-15 8e-08 -1.00
## Residual 1e-02 1e-01
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.759 0.022 75.000 35.3 <2e-16
## ecosystem_typeMedium unconnected 0.066 0.032 75.000 2.1 0.04
## scale(day) 0.042 0.017 75.000 2.5 0.01
## scale(water_addition_ml) 0.007 0.023 75.000 0.3 0.77
## scale(baseline) -0.007 0.015 75.000 -0.5 0.63
## scale(day):scale(water_addition_ml) 0.044 0.019 75.000 2.3 0.03
## scale(day):scale(baseline) -0.023 0.014 75.000 -1.7 0.10
##
## (Intercept) ***
## ecosystem_typeMedium unconnected *
## scale(day) *
## scale(water_addition_ml)
## scale(baseline)
## scale(day):scale(water_addition_ml) *
## scale(day):scale(baseline) .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) s():(_
## ecsystm_tMu -0.621
## scale(day) 0.101 -0.038
## scl(wtr_d_) 0.416 -0.173 0.493
## scale(bsln) -0.224 0.352 0.020 -0.021
## scl(d):(__) 0.598 -0.261 0.176 0.705 -0.104
## scl(dy):s() -0.048 0.020 -0.053 -0.109 0.003 -0.081
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Median Size
response_variable_selected = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
# --- PLOT ORIGINAL DATA --- #
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
response_variable_selected)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
# --- FILTER DATA --- #
filtered_data = ds_ecosystems %>%
filter(time_point %in% time_points_model,
ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected)),
!is.na(!!sym("water_addition_ml")))# --- PLOT FILTERED DATA --- #
plot.ecosystems.points(filtered_data,
ecosystem_type_selected,
response_variable_selected) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
# --- ADD BASELINES --- #
baselines = ds_ecosystems %>%
filter(time_point == time_point_of_baselines) %>%
select(culture_ID,
all_of(response_variable_selected)) %>%
rename(baseline = all_of(response_variable_selected))
filtered_data = filtered_data %>%
left_join(baselines)# --- COMPARE FULL, REDUCED, AND NULL MODEL --- #
full_model = lmer(get(response_variable_selected) ~
ecosystem_type * scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
reduced_model = lmer(get(response_variable_selected) ~
ecosystem_type +
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))
null_model = lmer(get(response_variable_selected) ~
scale(day) +
scale(water_addition_ml) * scale(day) +
scale(baseline) * scale(day) +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "bobyqa"))Full model vs null model
Full vs null model - ANOVA
# --- FULL VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(full_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 0.4 0.167 noneFull model - summary
# --- FULL MODEL - SHOW SUMMARY --- #
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type * scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1202.2 1230.0 -589.1 1178.2 63
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9 -0.5 0.0 0.4 3.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e+03 31
## day 6e+01 8 -1.00
## Residual 4e+05 611
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3701 115 30 32.2
## ecosystem_typeMedium unconnected 82 169 18 0.5
## scale(day) -234 106 61 -2.2
## scale(water_addition_ml) -161 122 70 -1.3
## scale(baseline) 202 78 17 2.6
## ecosystem_typeMedium unconnected:scale(day) 297 156 55 1.9
## scale(day):scale(water_addition_ml) 8 100 72 0.1
## scale(day):scale(baseline) 115 73 54 1.6
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeMedium unconnected 0.63
## scale(day) 0.03 *
## scale(water_addition_ml) 0.19
## scale(baseline) 0.02 *
## ecosystem_typeMedium unconnected:scale(day) 0.06 .
## scale(day):scale(water_addition_ml) 0.94
## scale(day):scale(baseline) 0.12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) e_Mu:( s():(_
## ecsystm_tMu -0.592
## scale(day) 0.142 -0.073
## scl(wtr_d_) 0.402 -0.166 0.492
## scale(bsln) -0.041 0.041 -0.001 -0.023
## ecsys_Mu:() -0.053 0.073 -0.585 -0.171 0.001
## scl(d):(__) 0.564 -0.226 0.167 0.708 -0.046 -0.037
## scl(dy):s() 0.021 -0.006 -0.038 -0.012 0.063 0.041 0.039
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Full model - residual plots
# --- FULL MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, full_model)qqnorm(resid(full_model))
qqline(resid(full_model))
Reduced vs null model
Reduced vs null model - ANOVA
# --- REDUCED VS NULL MODEL - SHOW MODEL STATS --- #
compute.model.stats(reduced_model,
null_model,
"mixed_model") %>%
show.tidy.model.stats(.)## deltaAIC p_value evidence
## 1 1.9 0.761 noneReduced model - summary
# --- REDUCED MODEL - SHOW SUMMARY --- #
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable_selected) ~ ecosystem_type + scale(day) +
## scale(water_addition_ml) * scale(day) + scale(baseline) *
## scale(day) + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1203.6 1229.1 -590.8 1181.6 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1 -0.4 0.1 0.4 3.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e+04 117
## day 1e+02 11 -1.00
## Residual 4e+05 626
## Number of obs: 75, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3712 116 35 32.0 <2e-16
## ecosystem_typeMedium unconnected 55 169 24 0.3 0.75
## scale(day) -115 89 54 -1.3 0.20
## scale(water_addition_ml) -120 123 71 -1.0 0.33
## scale(baseline) 202 78 19 2.6 0.02
## scale(day):scale(water_addition_ml) 13 103 73 0.1 0.90
## scale(day):scale(baseline) 109 75 43 1.4 0.16
##
## (Intercept) ***
## ecosystem_typeMedium unconnected
## scale(day)
## scale(water_addition_ml)
## scale(baseline) *
## scale(day):scale(water_addition_ml)
## scale(day):scale(baseline)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu scl(d) sc(__) scl(b) s():(_
## ecsystm_tMu -0.591
## scale(day) 0.148 -0.037
## scl(wtr_d_) 0.407 -0.158 0.487
## scale(bsln) -0.042 0.041 -0.001 -0.024
## scl(d):(__) 0.573 -0.229 0.181 0.715 -0.047
## scl(dy):s() 0.023 -0.009 -0.017 -0.005 0.079 0.040
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Reduced model - residual plots
# --- REDUCED MODEL - SHOW RESIDUAL PLOTS --- #
create.res.vs.fit.ecos(filtered_data, reduced_model)qqnorm(resid(reduced_model))
qqline(resid(reduced_model))
Populations
for(eco_type_i in 1:length(ecosystem_type_selected)){
print(ecosystem_type_selected[eco_type_i])
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_selected[eco_type_i]) %>%
group_by(day) %>%
summarise(Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Medium unconnected"
## [1] "Medium connected to medium"
Evaporation
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_selected,
"water_addition_ml")
Results
Meta-ecosystem diversity & function
We want here to plot the final paper version of the biodiversity and productivity of meta-ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to change the size of the plot.
# Define meta-ecosystems you want to plot.
metaecosystem_type_selected = c("Medium-Medium",
"Small-Large")# Write function to plot a response variable. Afterwards you can use this function to plot alpha, beta, gamma diversity, and biomass.
plot.single.plot = function(response_variable_selected){
ds_metaecosystems %>%
filter(metaecosystem_type %in% metaecosystem_type_selected,
!is.na(!!sym(response_variable_selected))) %>%
summarySE(measurevar = response_variable_selected,
groupvars = c("day", "metaecosystem_type", "connection")) %>%
ggplot(aes(x = day,
y = get(response_variable_selected),
group = interaction(day, metaecosystem_type, connection),
color = metaecosystem_type,
linetype = connection)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = interaction(metaecosystem_type, connection)),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
ymin = get(response_variable_selected) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable_selected],
color = "") +
scale_color_manual(values = treatment_colours) +
scale_linetype_manual(values = treatment_linetype) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm")) +
guides(color = guide_legend(title = NULL,
nrow = 2),
linetype = guide_legend(title = NULL,
nrow = 2)) +
theme(plot.margin = unit(c(ggarrange_margin_left,
ggarrange_margin_right,
ggarrange_margin_bottom,
ggarrange_margin_left),
"cm")) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
}# Combine plots of alpha, beta, gamma biodiversity and biomass.
p_combined = ggarrange(plot.single.plot("mean_shannon") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text", size = paper_labels_size) +
font("ylab", size = paper_labels_size),
plot.single.plot("bray_curtis") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("metaecosystem_richness") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("total_metaecosystem_bioarea_mm2") +
font("legend.text",
size = paper_labels_size) +
font("xlab",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size) +
scale_x_continuous(breaks = unique(ds_metaecosystems$day)),
heights = c(0.8, 0.8, 0.8, 1),
nrow = 4,
common.legend = TRUE,
align = "v",
labels = c("(a)", "(b)", "(c)", "(d)"),
label.x = 0.1,
label.y = 0.8) %>%
print()
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.Ecosystem diversity & function
We want here to plot the final paper version of the biodiversity and productivity of the small and large ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have the underscores in the legend. We don’t use underscores in the analysis because we can’t easily input them from a level name vector.
# Define ecosystems you want to plot.
ecosystem_type_selected = c("Small connected to large",
"Small connected to small",
"Small unconnected",
"Large connected to small",
"Large connected to large",
"Large unconnected")# Construct function to plot how the response variable (biomass or Shannon) of small and large ecosystems changes across time.
plot.single.plot = function(response_variable_selected){
ds_ecosystems %>%
filter(ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected))) %>%
summarySE(measurevar = response_variable_selected,
groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
ggplot(aes(x = day,
y = get(response_variable_selected),
group = interaction(day, ecosystem_type),
color = ecosystem_type,
linetype = ecosystem_type)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
ymin = get(response_variable_selected) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable_selected],
color = "") +
scale_color_manual(values = c("#993404",
"#993404",
"#993404",
"#3182bd",
"#3182bd",
"#3182bd"),
label = expression(S[L],
S[S],
S,
L[S],
L[L],
L)) +
scale_linetype_manual(values = c("solid",
"dashed",
"dotted",
"solid",
"dashed",
"dotted"),
label = expression(S[L],
S[S],
S,
L[S],
L[L],
L)) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
geom_hline(yintercept = 0,
color = zero_line_colour,
linetype = zero_line_line_type,
linewidth = zero_line_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm")) +
guides(color = guide_legend(title = NULL,
nrow = 3),
linetype = guide_legend(title = NULL,
nrow = 3)) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
}# Combine plots
p_combined = ggarrange(plot.single.plot("shannon") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("bioarea_mm2_per_ml") +
font("legend.text",
size = paper_labels_size) +
font("xlab",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size) +
scale_x_continuous(breaks = unique(ds_ecosystems$day)),
heights = c(0.8, 0.8, 1),
nrow = 2,
align = "v",
labels = c("(a)", "(b)"),
label.x = 0.1,
label.y = 0.8,
common.legend = TRUE) %>%
print()
We want here to plot the final paper version of the biodiversity and productivity of the medium ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have the underscores in the legend. We don’t use underscores in the analysis because we can’t easily input them from a level name vector.
# Define ecosystems you want to plot.
ecosystem_type_selected = c("Medium connected to medium",
"Medium unconnected")# Construct function to plot how the response variable (biomass or Shannon) of small and large ecosystems changes across time.
plot.single.plot = function(response_variable_selected){
ds_ecosystems %>%
filter(ecosystem_type %in% ecosystem_type_selected,
!is.na(!!sym(response_variable_selected))) %>%
summarySE(measurevar = response_variable_selected,
groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
ggplot(aes(x = day,
y = get(response_variable_selected),
group = interaction(day, ecosystem_type),
color = ecosystem_type,
linetype = ecosystem_type)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
ymin = get(response_variable_selected) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable_selected],
color = "") +
scale_color_manual(values = c("#d95f0e",
"#d95f0e"),
label = expression(M[M],
M)) +
scale_linetype_manual(values = c("dashed",
"dotted"),
label = expression(M[M],
M)) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
geom_hline(yintercept = 0,
color = zero_line_colour,
linetype = zero_line_line_type,
linewidth = zero_line_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm")) +
guides(color = guide_legend(title = NULL,
nrow = 3),
linetype = guide_legend(title = NULL,
nrow = 3)) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
}# Combine plots
p_combined = ggarrange(plot.single.plot("shannon") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("bioarea_mm2_per_ml") +
font("legend.text",
size = paper_labels_size) +
font("xlab",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size) +
scale_x_continuous(breaks = unique(ds_ecosystems$day)),
heights = c(0.8, 0.8, 1),
nrow = 2,
align = "v",
labels = c("(a)", "(b)"),
label.x = 0.1,
label.y = 0.8,
common.legend = TRUE) %>%
print()
Ecosystem autotrophic/heterotrophic ratio
We want here to plot the final paper version of the ratio between autotrophic and heterotrophic biomass in small, medium, and large unconnected ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have S, M, and L in the legend.
# Define ecosystems and response variable you want to plot.
ecosystem_type_input = c("S",
"M",
"L")
response_variable = "auto_hetero_ratio"# Construct plot
p = ds_ecosystems %>%
# Manipulate
mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
ecosystem_type == "Medium unconnected" ~ "M",
ecosystem_type == "Large unconnected" ~ "L")) %>%
filter(ecosystem_type %in% ecosystem_type_input,
!is.na(!!sym(response_variable))) %>%
summarySE(measurevar = response_variable,
groupvars = c("day", "ecosystem_type", "ecosystem_size", "connection")) %>%
# Create plot
ggplot(aes(x = day,
y = get(response_variable),
group = interaction(day, ecosystem_type),
color = ecosystem_type)) +
# Points
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_errorbar(aes(ymax = get(response_variable) + ci,
ymin = get(response_variable) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
# Lines
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
# Axes and legend
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable],
color = "") +
scale_x_continuous(breaks = unique(ds_ecosystems$day)) +
guides(color = guide_legend(title = NULL,
nrow = 1),
linetype = guide_legend(title = NULL,
nrow = 1)) +
scale_color_manual(values = c("#000000",
"#737373",
"#bdbdbd")) +
# Extra graphic elements
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"),
axis.title.x = element_text(size = paper_labels_size),
axis.title.y = element_text(size = paper_labels_size),
legend.text = element_text(size = paper_labels_size)) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color) +
geom_hline(yintercept = 0,
color = zero_line_colour,
linetype = zero_line_line_type,
linewidth = zero_line_line_width) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width)
p
Evaporation
During the experiment we noticed that microwaving ecosystem sub-samples for three minutes to create disturbance caused the evaporation of the ecosystems. However, we don’t know exactly how much evaporated and how much we should refill the ecosystems to bring them back to the original volume. Therefore, here I quantify the evaporation of 5.75 and 6.75 ml of deionised water, which represent low and high disturbance, respectively. For each disturbance level, I microwaved 15 tubes of that disturbance level for three minutes and measured their evaporation. To do so, I weighed the water before the microwaving (weigh tubes, add water, reweigh tubes) and after it (weigh Becker, pour water into it, reweigh Becker).
evaporation.test = read.csv(here("1_experiment", "evaporation_test","evaporation_test_initial.csv"), header = TRUE)
evaporation.test %>%
ggplot(aes (x = as.character(water_pipetted),
y = weight_water_evaporated,
group = interaction(water_pipetted, as.character(rack)),
fill = as.character(rack))) +
geom_boxplot(width = boxplot_width) +
labs(x = "Water volume (ml)" ,
y = "Evaporation (g)",
fill = "Rack replicate")
Furthermore, during the experiment we noticed that microwaving five 6.75 ml ecosystems sub-samples with ten empty tubes for three minutes to create disturbance caused the evaporation of the sub-samples more than if they were with other sub-samples. However, we don’t know exactly how much evaporated and how much we should refill the ecosystems to bring them back to the original volume. Therefore, here I quantify the evaporation of five 6.75 ml sub-samples with ten empty or filled falcon tubes. The weighting was conducted as above.
evaporation.test = read.csv(here("1_experiment", "evaporation_test", "evaporation_test_fill_nofill.csv"), header = TRUE)
evaporation.test %>%
ggplot(aes (x = all_tubes_water,
y = weight_water_evaporated)) +
geom_boxplot(width = boxplot_width) +
labs(x = "Water in the other 10 tubes" ,
y = "Evaporation (g)")
Analysis scripts
Video analysis
To analyse the videos I took of the ecosystems, I used the package BEMOVI. For this, I had to use the powerful computer. Below is the code utilised for video analysis on the powerful computer.
# Clear workspace
rm(list = ls())
# Set working directory
setwd("/media/mendel-himself/ID_061_Ema2/PatchSizePilot/training")
# Load required libraries
# library(devtools)
# install_github("femoerman/bemovi", ref="master")
library(bemovi)
library(parallel)
library(doParallel)
library(foreach)
# Define memory allocation parameters (in MB)
memory.alloc <- 240000 # Total memory allocated
memory.per.identifier <- 40000 # Memory per identifier
memory.per.linker <- 5000 # Memory per linker
memory.per.overlay <- 60000 # Memory per overlay
# Set paths for tools and particle linker
tools.path <- "/home/mendel-himself/bemovi_tools/" # Path to tools folder
to.particlelinker <- tools.path
# Set directories and file names
to.data <- paste(getwd(), "/", sep = "")
video.description.folder <- "0_video_description/"
video.description.file <- "video_description.txt"
raw.video.folder <- "1_raw/"
raw.avi.folder <- "1a_raw_avi/"
metadata.folder <- "1b_raw_meta/"
particle.data.folder <- "2_particle_data/"
trajectory.data.folder <- "3_trajectory_data/"
temp.overlay.folder <- "4a_temp_overlays/"
overlay.folder <- "4_overlays/"
merged.data.folder <- "5_merged_data/"
ijmacs.folder <- "ijmacs/"
######################################################################
# VIDEO PARAMETERS
# Define video parameters
fps <- 25 # Video frame rate (frames per second)
total_frames <- 125 # Total length of video (frames)
width <- 2048 # Video width (pixels)
height <- 2048 # Video height (pixels)
measured_volume <- 34.4 # Measured volume (microliters) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
pixel_to_scale <- 4.05 # Size of a pixel (micrometers) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
video.format <- "cxd" # Video file format (avi, cxd, mov, tiff)
difference.lag <- 10 # Difference lag
thresholds <- c(13, 255) # Threshold values of pixel intensity (considered a measure of pixel "whiteness") for determining if a pixel belongs to an individual rather than the background
######################################################################
# FILTERING PARAMETERS
# optimized for Perfex Pro 10 stereomicrocope with Perfex SC38800 (IDS UI-3880LE-M-GL) camera
# tested stereomicroscopes: Perfex Pro 10, Nikon SMZ1500, Leica M205 C
# tested cameras: Perfex SC38800, Canon 5D Mark III, Hamamatsu Orca Flash 4
# tested species: Tet, Col, Pau, Pca, Eug, Chi, Ble, Ceph, Lox, Spi
particle_min_size <- 10 # Minimum particle size (pixels)
particle_max_size <- 1000 # Maximum particle size (pixels)
trajectory_link_range <- 3 # Number of adjacent frames for linking particles
trajectory_displacement <- 16 # Maximum displacement of a particle between frames
# Filtering criteria
filter_min_net_disp <- 25 # Minimum net displacement (µm)
filter_min_duration <- 1 # Minimum duration (s)
filter_detection_freq <- 0.1 # Minimum detection frequency (1/s)
filter_median_step_length <- 3 # Minimum median step length (µm)
######################################################################
# VIDEO ANALYSIS
# Check if all tools are installed and set permissions
check_tools_folder(tools.path)
system(paste0("chmod a+x ", tools.path, "bftools/bf.sh"))
system(paste0("chmod a+x ", tools.path, "bftools/bfconvert"))
system(paste0("chmod a+x ", tools.path, "bftools/showinf"))
# Convert video files to compressed avi format
convert_to_avi(to.data,
raw.video.folder,
raw.avi.folder,
metadata.folder,
tools.path,
fps,
video.format)
# Uncomment the following lines for testing
# check_video_file_names(to.data, raw.avi.folder, video.description.folder, video.description.file)
# check_threshold_values(to.data, raw.avi.folder, ijmacs.folder, 2, difference.lag, thresholds, tools.path, memory.alloc)
# Identify particles in the video
locate_and_measure_particles(to.data,
raw.avi.folder,
particle.data.folder,
difference.lag,
min_size = particle_min_size,
max_size = particle_max_size,
thresholds = thresholds,
tools.path,
memory = memory.alloc,
memory.per.identifier = memory.per.identifier,
max.cores = detectCores() - 1)
# Link particles across frames to form trajectories
link_particles(to.data,
particle.data.folder,
trajectory.data.folder,
linkrange = trajectory_link_range,
disp = trajectory_displacement,
start_vid = 1,
memory = memory.alloc,
memory_per_linkerProcess = memory.per.linker,
raw.avi.folder,
max.cores = detectCores() - 1,
max_time = 1)
# Merge video description file with particle data
merge_data(to.data,
particle.data.folder,
trajectory.data.folder,
video.description.folder,
video.description.file,
merged.data.folder)
# Load the merged data
load(paste0(to.data, merged.data.folder, "Master.RData"))
# Filter trajectory data based on defined criteria
trajectory.data.filtered <- filter_data(trajectory.data,
filter_min_net_disp,
filter_min_duration,
filter_detection_freq,
filter_median_step_length)
# Summarize trajectory data to individual-based data
morph_mvt <- summarize_trajectories(trajectory.data.filtered,
calculate.median = F,
write = T,
to.data,
merged.data.folder)
# Summarize sample level data
summarize_populations(trajectory.data.filtered,
morph_mvt,
write = T,
to.data,
merged.data.folder,
video.description.folder,
video.description.file,
total_frames)
# Create overlays for validation
create.subtitle.overlays(to.data,
traj.data = trajectory.data.filtered,
raw.video.folder,
raw.avi.folder,
temp.overlay.folder,
overlay.folder,
fps,
vid.length = total_frames / fps,
width,
height,
tools.path = tools.path,
overlay.type = "number",
video.format)
# Create overlays (old method)
create_overlays(traj.data = trajectory.data.filtered,
to.data = to.data,
merged.data.folder = merged.data.folder,
raw.video.folder = raw.avi.folder,
temp.overlay.folder = "4a_temp_overlays_old/",
overlay.folder = "4_overlays_old/",
width = width,
height = height,
difference.lag = difference.lag,
type = "traj",
predict_spec = F,
contrast.enhancement = 1,
IJ.path = "/home/mendel-himself/bemovi_tools",
memory = memory.alloc,
max.cores = detectCores() - 1,
memory.per.overlay = memory.per.overlay)Species identification
To avoid transferring all the data from the powerful computer, I performed species identification on that system and subsequently imported the results into the Rstudio folder on my personal computer. Below is the code utilised for species identification on the powerful computer.
# Clear the workspace
rm(list = ls())
# Uncomment and install required packages if not already installed
#install.packages("e1071",dependencies = T)
#install.packages("devtools",dependencies = T)
#install_github("pennekampster/bemovi", ref="master")
#library(devtools)
# Load required libraries
library(bemovi)
library(e1071)
library("here")
library("tidyverse")
# Define time points in the experiment
time_points_in_experiment = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")
# Loop through each time point in the experiment
for (time_point in time_points_in_experiment) {
# Define folder names and paths
video.description.folder = "0_video_description/"
video.description.file = "video_description.txt"
merged.data.folder = "5_merged_data/"
monocultures_folder_path = here("biomass_analysis", "training", "")
mixed_cultures_folder_path = here("biomass_analysis", time_point, "")
#Parameters used in the video analysis script
fps = 25
nsv = 5
measured_volume = 34.4
pixel_to_scale = 4.05
filter_min_net_disp = 25
filter_min_duration = 1
filter_detection_freq = 0.1
filter_median_step_length = 3
# Load master dataset of mono-cultures
load(paste0(monocultures_folder_path, merged.data.folder, "Master.RData"))
trajectory.data_monocultures = trajectory.data
rm(trajectory.data)
# Filter the master data of mono-cultures using the same parameters as in the video analysis script
trajectory.data_monocultures.filtered = filter_data(trajectory.data_monocultures,
filter_min_net_disp,
filter_min_duration,
filter_detection_freq,
filter_median_step_length)
# Summarize trajectory data to individual-based data
morph_mvt = summarize_trajectories(data = trajectory.data_monocultures.filtered,
calculate.median = FALSE,
write = TRUE,
to.data = monocultures_folder_path,
merged.data.folder = merged.data.folder) %>%
mutate(comment = NULL)
# Prepare training data by removing incomplete cases
training_data = morph_mvt[complete.cases(morph_mvt), ]
# Train SVM model on the training data
svm1 = svm(
factor(species) ~
mean_grey +
sd_grey +
mean_area +
sd_area +
mean_perimeter +
mean_turning +
sd_turning +
sd_perimeter +
mean_major +
sd_major +
mean_minor +
sd_minor +
mean_ar +
sd_ar +
duration +
max_net +
net_disp +
net_speed +
gross_disp +
max_step +
min_step +
sd_step +
sd_gross_speed +
max_gross_speed +
min_gross_speed ,
data = training_data,
probability = T,
na.action = na.pass)
# Generate and print confusion matrix
confusion.matrix = table(svm1$fitted, training_data$species)
confusion.matrix.nd = confusion.matrix
diag(confusion.matrix.nd) = 0
svm1$confusion = cbind(confusion.matrix,
class.error = rowSums(confusion.matrix.nd) / rowSums(confusion.matrix))
print(paste("Confusion matrix of time point", time_point))
print(svm1$confusion)
# Extract unique species names
species.names = unique(trajectory.data_monocultures$species)
# Load mixed cultures dataset
load(paste0(mixed_cultures_folder_path, merged.data.folder, "Master.RData"))
trajectory.data_mixed = trajectory.data
rm(trajectory.data)
# Filter mixed cultures data using the same parameters
trajectory.data_mixed.filtered = filter_data(trajectory.data_mixed,
filter_min_net_disp,
filter_min_duration,
filter_detection_freq,
filter_median_step_length)
# Summarize trajectory data to individual-based data
morph_mvt = summarize_trajectories(data = trajectory.data_mixed.filtered,
calculate.median = FALSE,
write = TRUE,
to.data = mixed_cultures_folder_path,
merged.data.folder = merged.data.folder)[, which(colnames(morph_mvt) != "Col_manual")] %>%
mutate(comment = NULL)
# Prepare data for prediction by removing incomplete cases
data.to.predict = morph_mvt[complete.cases(morph_mvt),]
# Predict species using the trained SVM model
p.id = predict(object = svm1, data.to.predict, type = "response")
data.to.predict$predicted_species = as.character(p.id)
# Summarize population data
pop.data = summarize_populations(traj.data = trajectory.data_monocultures.filtered,
sum.data = morph_mvt,
write = TRUE,
to.data = mixed_cultures_folder_path,
merged.data.folder = merged.data.folder,
video.description.folder = video.description.folder,
video.description.file = video.description.file,
total_frame = fps * nsv)
# Function to calculate species density
species.density = function(sample_output,
indiv_predicted,
species_names,
total_frames,
mv = measured_volume) {
samples = unique(indiv_predicted$file)
sp.dens = matrix(0,
nrow(sample_output),
length(species_names))
colnames(sp.dens) = species_names
for (i in 1:length(samples)) {
indiv = subset(indiv_predicted, file == samples[i])
spec = unique(indiv$predicted_species)
for (j in 1:length(spec)) {
all.indiv.sp = subset(indiv,
predicted_species == spec[j])
dens = sum(all.indiv.sp$N_frames) / total_frames / mv
sp.dens[which(sample_output$file == as.character(samples[i])), which(species_names == spec[j])] = dens
}
}
return(cbind(sample_output, sp.dens))
}
# Calculate species density for the current time point
output = species.density(pop.data,
data.to.predict,
species.names,
total_frames = fps * nsv,
mv = measured_volume)
# Save the species density results to a CSV file
file_name = paste0("species_ID_", time_point, ".csv")
write.csv(output, here("biomass_analysis", "species_ID_results", file_name))
rm(output)
}Other
Running time
## Time difference of 1.9 minsDisturbance input
Check that disturbance_global_selected is what you set:
print(paste0("Disturbance = ", disturbance_global_selected))## [1] "Disturbance = low"Useful code
If you want to change a certain part of the code using the following code in Unix:
#Rmd script
cd /Users/Ema/Documents/Github/PatchSize/3_r_files
sed -i '' 's/old_string/new_string/g' *.Rmd
#R script
cd /Users/ema/Documents/GitHub/PatchSize/3_r_files/functions
sed -i '' 's/old_string/new_string/g' *.Ryou want to share a dataset and get a reproducible object, use the following R code:
dput()Crashed cultures
The only type of ecosystem where all cultures crashed was small connected to small at high disturbance.
R version
R.version.string## [1] "R version 4.3.2 (2023-10-31)"R package versions
The R packages we used with their version are as follows:
sessionInfo()## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.2.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Europe/Zurich
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices datasets utils methods base
##
## other attached packages:
## [1] conflicted_1.2.0 broom.mixed_0.2.9.5 emmeans_1.10.4
## [4] combinat_0.0-8 Rmisc_1.5.1 betapart_1.6
## [7] vegan_2.6-6.1 lattice_0.22-6 permute_0.9-7
## [10] glmmTMB_1.1.10 lmerTest_3.1-3 lme4_1.1-35.4
## [13] Matrix_1.6-5 GGally_2.2.1 gridExtra_2.3
## [16] plotly_4.10.4 ggpubr_0.6.0 lubridate_1.9.3
## [19] forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
## [22] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1
## [25] tibble_3.2.1 ggplot2_3.5.1 tidyverse_2.0.0
## [28] plyr_1.8.9 renv_1.0.7.9000 testthat_3.2.1.1
## [31] here_1.0.1
##
## loaded via a namespace (and not attached):
## [1] RColorBrewer_1.1-3 rstudioapi_0.16.0 jsonlite_1.8.8
## [4] magrittr_2.0.3 estimability_1.5.1 farver_2.1.2
## [7] nloptr_2.1.1 rmarkdown_2.27 vctrs_0.6.5
## [10] memoise_2.0.1 minqa_1.2.7 rstatix_0.7.2
## [13] htmltools_0.5.8.1 itertools_0.1-3 broom_1.0.6
## [16] pracma_2.4.4 sass_0.4.9 parallelly_1.38.0
## [19] bslib_0.7.0 htmlwidgets_1.6.4 desc_1.4.3
## [22] cachem_1.1.0 TMB_1.9.15 lifecycle_1.0.4
## [25] minpack.lm_1.2-4 iterators_1.0.14 pkgconfig_2.0.3
## [28] optimx_2023-10.21 R6_2.5.1 fastmap_1.2.0
## [31] rbibutils_2.2.16 future_1.34.0 magic_1.6-1
## [34] digest_0.6.36 numDeriv_2016.8-1.1 colorspace_2.1-0
## [37] furrr_0.3.1 rprojroot_2.0.4 pkgload_1.3.4
## [40] crosstalk_1.2.1 labeling_0.4.3 fansi_1.0.6
## [43] timechange_0.3.0 httr_1.4.7 abind_1.4-5
## [46] mgcv_1.9-0 compiler_4.3.2 withr_3.0.0
## [49] backports_1.5.0 carData_3.0-5 ggstats_0.6.0
## [52] highr_0.11 ggsignif_0.6.4 MASS_7.3-60
## [55] tools_4.3.2 ape_5.8 glue_1.7.0
## [58] rcdd_1.6 nlme_3.1-163 grid_4.3.2
## [61] cluster_2.1.4 generics_0.1.3 snow_0.4-4
## [64] gtable_0.3.5 tzdb_0.4.0 data.table_1.15.4
## [67] hms_1.1.3 car_3.1-2 utf8_1.2.4
## [70] foreach_1.5.2 pillar_1.9.0 splines_4.3.2
## [73] tidyselect_1.2.1 knitr_1.47 reformulas_0.3.0
## [76] xfun_0.45 brio_1.1.5 stringi_1.8.4
## [79] lazyeval_0.2.2 yaml_2.3.8 boot_1.3-30
## [82] evaluate_0.24.0 codetools_0.2-20 cli_3.6.3
## [85] geometry_0.4.7 Rdpack_2.6.1 munsell_0.5.1
## [88] jquerylib_0.1.4 Rcpp_1.0.12 doSNOW_1.0.20
## [91] globals_0.16.3 coda_0.19-4.1 parallel_4.3.2
## [94] picante_1.8.2 listenv_0.9.1 viridisLite_0.4.2
## [97] mvtnorm_1.3-1 scales_1.3.0 rlang_1.1.4
## [100] cowplot_1.1.3 fastmatch_1.1-4 waldo_0.5.2Before submitting
- Take off the holistic models
- Update that you took off the third time point
- Comment code
References
Bates, Douglas, Martin Mächler, Benjamin M. Bolker, and Steven C.
Walker. 2015. “Fitting Linear Mixed-Effects Models Using
Lme4.” Journal of Statistical Software 67. https://doi.org/10.18637/jss.v067.i01.